Short answer

No. No Muslim may punish anyone himself, for blasphemy or for any other crime. In Islamic law, punishment belongs only to a lawful court, after proof and a fair trial. Scholars agree that even a murderer may be punished only by lawful authority. An accused person may be innocent, or may have been misheard. A man who kills on his own kills someone no court has found guilty. The Qur'an says killing a believer on purpose earns Hell. The Prophet (ﷺ) said whoever kills a non-Muslim living under a treaty will not smell Paradise. Wherever a Muslim lives, he must keep that country's law (17:34). So such a man faces a murder charge in this world, and God's (﷾) judgement in the next. The Prophet (ﷺ) himself bore insults with patience.

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