Short answer
No. Qur'an 5:68 names three things, not two: the Torah, the Injil (the Gospel Jesus preached), and the revelation that has come from their Lord. In Arabic, the verse before it uses the same words for the revelation given to the Prophet Muhammad (ﷺ). So 5:68 calls them to the Qur'an too, not away from it. The early commentator al-Tabari says the third thing is the Qur'an. Ibn Kathir explains that the Torah and the Injil, truly followed, command belief in Muhammad (ﷺ). The Qur'an says he is mentioned in both. Qur'an 10:94 is spoken to the Prophet (ﷺ) himself, and it begins with "if". Ibn Kathir says this does not mean he ever doubted. It calls those who read the earlier Book as witnesses that the message is true, not as guides to follow. Islam's answer: neither verse tells anyone to obey the Bible as it stands today.
Full explanation
Qur'an 5:68 names three things
The verse lists the Torah, the Injil and a third thing: "all the revelation that has come to you from your Lord". One verse earlier, the Prophet (ﷺ) is told to proclaim what "hath been sent to thee from thy Lord". Later in 5:68 itself, that revelation is said to increase many of them in rebellion and disbelief. In Arabic the wording is the same each time, ma unzila (what has been sent down), with only the person addressed changing. So the third thing, all the revelation from their Lord, includes the Qur'an. The early commentator al-Tabari (9th to 10th century) says it is the Qur'an.
“Say: "O People of the Book! ye have no ground to stand upon unless ye stand fast by the Law, the Gospel, and all the revelation that has come to you from your Lord." It is the revelation that cometh to thee from thy Lord, that increaseth in most of them their obstinate rebellion and blasphemy. But sorrow thou not over (these) people without Faith.”
“O Messenger! proclaim the (message) which hath been sent to thee from thy Lord. If thou didst not, thou wouldst not have fulfilled and proclaimed His mission. And Allah will defend thee from men (who mean mischief). For Allah guideth not those who reject Faith.”
Explains 'what has been sent down to you from your Lord' as the Furqan, the Qur'an, that Muhammad (ﷺ) brought them, and says the People of the Book must act on all of it, including its call to believe in him.
Truly followed, the earlier books lead to him
Ibn Kathir, a commentator of the 14th century, explains the verse this way. The People of the Book (Jews and Christians) have no footing until they act on all that God (﷾) revealed. The Torah and the Injil themselves command belief in the Prophet (ﷺ). The Qur'an says the same: those who truly follow him are those who find him mentioned in the Torah and the Injil they hold. So standing by those books, in the Qur'an's sense, means accepting the Qur'an. Like 5:47, the verse asks them to act on what God (﷾) sent down, the revelation that survives in those books, not on words men added. The passage around 5:47 shows this. Some Jews brought an adultery case to the Prophet (ﷺ), hoping for a lighter ruling than the stoning in their own Torah. A companion of the Prophet (ﷺ) says 5:41, 5:44, 5:45 and 5:47 came down about this. The full account is on "Does the 'Islamic dilemma' prove the Qur'an wrong?".
Explains that the People of the Book have no true standing until they believe in and act on all the books God revealed to the prophets, and that those books themselves command following Muhammad (ﷺ) and believing in his prophethood.
“"Those who follow the messenger, the unlettered Prophet, whom they find mentioned in their own (scriptures),- in the law and the Gospel;- for he commands them what is just and forbids them what is evil; he allows them as lawful what is good (and pure) and prohibits them from what is bad (and impure); He releases them from their heavy burdens and from the yokes that are upon them. So it is those who believe in him, honour him, help him, and follow the light which is sent down with him,- it is they who will prosper."”
“Let the people of the Gospel judge by what Allah hath revealed therein. If any do fail to judge by (the light of) what Allah hath revealed, they are (no better than) those who rebel.”
“But why do they come to thee for decision, when they have (their own) law before them?- therein is the (plain) command of Allah; yet even after that, they would turn away. For they are not (really) People of Faith.”
Abdullah ibn Umar reports that Jews brought a case of adultery to the Prophet (ﷺ). He asked what the Torah said about stoning. They said they exposed and flogged the guilty. Abdullah ibn Salam said they were lying. The Torah was brought, and the reader covered the verse of stoning with his hand. Told to lift it, he did, and the verse was there. The Prophet (ﷺ) then ordered both to be stoned.
Al-Bara' ibn Azib reports that a Jewish scholar, asked under oath, admitted that the Torah prescribed stoning for adultery. They had been sparing the rich and punishing the poor, so they agreed on blackening the face and flogging instead. The Prophet (ﷺ) said he was the first to revive Allah's command after they had let it die. Al-Bara' says Qur'an 5:41 came down about this: they had said, go to Muhammad and accept flogging, but avoid a verdict of stoning. Then 5:44, 5:45 and 5:47 were sent down, all of them, he says, about the unbelievers.
Qur'an 10:94 begins with "if"
The verse is spoken to the Prophet (ﷺ), not to Muslims in general. It is a condition: it begins with "if". It ends by telling him that the truth has come to him from his Lord, so he should not doubt. Ibn Kathir, explaining the matching words in 6:114, says this is a conditional statement. It does not mean that doubt ever came to the Prophet (ﷺ).
“If thou wert in doubt as to what We have revealed unto thee, then ask those who have been reading the Book from before thee: the Truth hath indeed come to thee from thy Lord: so be in no wise of those in doubt.”
“Say: "Shall I seek for judge other than Allah? - when He it is Who hath sent unto you the Book, explained in detail." They know full well, to whom We have given the Book, that it hath been sent down from thy Lord in truth. Never be then of those who doubt.”
Explains "fulfilled in truth and in justice" through Qatadah: truth in what God has stated and justice in what He has decided. Explains "none can change His words" as: no one can turn back God's judgement, whether in this life or in the Hereafter. On "never be then of those who doubt" (6:114) he compares 10:94 and explains that it is a conditional statement, which does not mean that doubt ever occurred to the Prophet (ﷺ).
Witnesses, not guides
What the readers of the earlier Book are asked to confirm is that the Qur'an's message was known to them. The Qur'an says the same elsewhere. It is announced in the books of earlier peoples, and the learned of the Children of Israel (the Jews) knew it to be true. A court that calls a witness does not hand him the judgement.
“Without doubt it is (announced) in the mystic Books of former peoples. Is it not a Sign to them that the Learned of the Children of Israel knew it (as true)?”
“Say: "Shall I seek for judge other than Allah? - when He it is Who hath sent unto you the Book, explained in detail." They know full well, to whom We have given the Book, that it hath been sent down from thy Lord in truth. Never be then of those who doubt.”
The same Qur'an says the text in their hands was altered
The Qur'an that mentions the Torah and the Injil also says that some wrote a book with their own hands and called it God's (﷾). It says some displaced words from their places. It says some forgot a good part of what was sent to them. The same surah as 5:68 says it twice: some change words from their places (5:13, 5:41). Ibn Abbas, the Prophet's (ﷺ) cousin, said the People of the Book changed their scripture. He said they wrote it with their own hands and called it from Allah (﷾). Where the Qur'an speaks to the People of the Book about their scripture, it tells them to bring the Law and study it. That is the language of calling for evidence, not of submitting to it. So the Qur'an confirms the revelation God (﷾) sent, not every word of the text in their hands. It calls itself a witness over that earlier scripture.
“Then woe to those who write the Book with their own hands, and then say:"This is from Allah," to traffic with it for miserable price!- Woe to them for what their hands do write, and for the gain they make thereby.”
“Of the Jews there are those who displace words from their (right) places, and say: "We hear and we disobey"; and "Hear what is not Heard"; and "Ra'ina"; with a twist of their tongues and a slander to Faith. If only they had said: "What hear and we obey"; and "Do hear"; and "Do look at us"; it would have been better for them, and more proper; but Allah hath cursed them for their Unbelief; and but few of them will believe.”
“From those, too, who call themselves Christians, We did take a covenant, but they forgot a good part of the message that was sent them: so we estranged them, with enmity and hatred between the one and the other, to the day of judgment. And soon will Allah show them what it is they have done.”
“But because of their breach of their covenant, We cursed them, and made their hearts grow hard; they change the words from their (right) places and forget a good part of the message that was sent them, nor wilt thou cease to find them- barring a few - ever bent on (new) deceits: but forgive them, and overlook (their misdeeds): for Allah loveth those who are kind.”
“O Messenger! let not those grieve thee, who race each other into unbelief: (whether it be) among those who say "We believe" with their lips but whose hearts have no faith; or it be among the Jews,- men who will listen to any lie,- will listen even to others who have never so much as come to thee. They change the words from their (right) times and places: they say, "If ye are given this, take it, but if not, beware!" If any one's trial is intended by Allah, thou hast no authority in the least for him against Allah. For such - it is not Allah's will to purify their hearts. For them there is disgrace in this world, and in the Hereafter a heavy punishment.”
“All food was lawful to the Children of Israel, except what Israel Made unlawful for itself, before the Law (of Moses) was revealed. Say: "Bring ye the Law and study it, if ye be men of truth."”
“To thee We sent the Scripture in truth, confirming the scripture that came before it, and guarding it in safety: so judge between them by what Allah hath revealed, and follow not their vain desires, diverging from the Truth that hath come to thee. To each among you have we prescribed a law and an open way. If Allah had so willed, He would have made you a single people, but (His plan is) to test you in what He hath given you: so strive as in a race in all virtues. The goal of you all is to Allah; it is He that will show you the truth of the matters in which ye dispute;”
Ibn Abbas said to the Muslims: why do you ask the People of the Book about anything, when your Book, revealed to the Messenger of Allah (ﷺ), is the newest and you read it pure and unchanged? Allah has told you that they changed the Book of Allah and altered it, wrote the Book with their own hands and said it was from Allah, to sell it for a little gain. Does the knowledge that has come to you not keep you from asking them? He added that, by Allah, they had never seen a man of them ask the Muslims about what was revealed to them. The same report is in Bukhari 2685.
Verse by verse
Qur'an 5:68 — Surat al-Ma'ida (The Table), verse 68
“Say: "O People of the Book! ye have no ground to stand upon unless ye stand fast by the Law, the Gospel, and all the revelation that has come to you from your Lord." It is the revelation that cometh to thee from thy Lord, that increaseth in most of them their obstinate rebellion and blasphemy. But sorrow thou not over (these) people without Faith.”
Cited for
The Qur'an tells Jews and Christians to stand by the Torah and the Injil, so the Bible they hold is still valid.
The response
The verse adds a third thing, the revelation from their Lord. The Qur'an uses the same Arabic phrase, ma unzila (what has been sent down), for the Prophet's (ﷺ) revelation in 5:67 and in 5:68. Ibn Kathir explains that the earlier books, truly followed, command belief in the Prophet (ﷺ). Qur'an 7:157 says they find him mentioned in the Torah and the Injil.
Where it lands — The verse calls its hearers to the Qur'an too, so it cannot tell them to keep the Bible instead.
Qur'an 10:94 — Surat Yunus (Jonas), verse 94
“If thou wert in doubt as to what We have revealed unto thee, then ask those who have been reading the Book from before thee: the Truth hath indeed come to thee from thy Lord: so be in no wise of those in doubt.”
Cited for
The Qur'an tells Muhammad (ﷺ) to ask Jews and Christians when in doubt, so their Book was reliable.
The response
The verse is a condition spoken to the Prophet (ﷺ). It ends by telling him the truth has come to him from his Lord, so he should not doubt. Ibn Kathir says the condition does not mean he ever doubted. The People of the Book are called as witnesses, as in 26:197, where the learned of Israel knew the message to be true.
Where it lands — The verse asks for testimony that the message was foretold, not obedience to the Bible as it stands.
Perspectives
Christian reading
The Qur'an tells Jews and Christians to stand by the Torah and the Injil. It tells the Prophet Muhammad (ﷺ) to ask them when in doubt. On this reading the Qur'an confirms the Bible as it was in the 7th century. Christians say that is the Bible they hold today.
Christians read 5:68 as a command to Jews and Christians to keep the Bible they hold.
Rebuttal
The verse names a third thing, the revelation from their Lord, in the words 5:67 uses for the Prophet's (ﷺ) revelation. Truly followed, the Law and the Injil lead to the Qur'an. The same surah says some changed words from their places (5:13, 5:41), so it cannot mean every word they hold.
Christians read 10:94 as proof that the Qur'an treats the Bible as reliable enough to settle Muhammad's (ﷺ) doubts.
Rebuttal
The verse is a condition, and it ends by telling the Prophet (ﷺ) the truth has already come to him. Ibn Kathir says this does not mean he ever doubted. Those who read the earlier Book are called as witnesses that the message was foretold. They are not called to vouch for every word they hold.
The Islamic perspective
Qur'an 5:68 calls the People of the Book to the Torah, the Injil and the Qur'an together. The earlier books, truly followed, point to the Prophet (ﷺ). Qur'an 10:94 is a condition addressed to the Prophet (ﷺ) that calls the People of the Book as witnesses. Neither verse tells anyone to follow the Bible as it now stands.
Qur'an 5:68 names three things: the Torah, the Injil, and the revelation that has come from the Lord.
The Qur'an uses the same Arabic words in 5:67 and 5:68: what has been sent down from your Lord. In both it means the Prophet's (ﷺ) revelation.
Al-Tabari explains the third thing in 5:68 as the Qur'an that the Prophet (ﷺ) brought.
Ibn Kathir explains that the Torah and the Injil command following Muhammad (ﷺ) and believing in his prophethood.
The Qur'an states that the Prophet (ﷺ) is found mentioned in the Torah and the Injil.
Qur'an 10:94 is a condition addressed to the Prophet (ﷺ). It ends by telling him the truth has come to him from his Lord, so he should not doubt.
Ibn Kathir explains this conditional wording as never meaning that the Prophet (ﷺ) actually doubted.
The Qur'an calls the learned of the Children of Israel as witnesses that its message was known in earlier scripture.
The same Qur'an says some of the People of the Book wrote scripture with their own hands, displaced words and forgot part of the message. It asks them to bring the Law as evidence.
The same surah, al-Ma'ida, says some change words from their places (5:13, 5:41).
Qur'an 5:43 says the Torah they held still had God's (﷾) ruling on the case they brought. The Qur'an confirms what survives of the revelation, not every word.
A companion explains why Qur'an 5:41, 5:44, 5:45 and 5:47 came down. It was about Jews who sought to avoid the stoning ruling in their own Torah.