There is no provision for punishment of stoning to death in the Quran, but it is described who deserves the stone-pelting punishment in the Sunnah.
The Quran contains the message, teachings, and laws of Allah that are said to be conveyed by Allah's words, while Sunnah refers to the prophet Muhammad's sayings and practices. Quran and Sunnah are two vital sources of Islamic legislation.
Stoning is a form of capital punishment in which the convicted criminal is put to death by having stones thrown at them, generally by a crowd. In Sunnah, stoning is mostly linked to adultery crimes. The Quran (24:2 Surah a Nur) mentions only lashing as punishment for adultery (Refer Page No.4, La Strada International Association).
In Sunnah, the prescription for the punishment of premarital and extramarital adultery differs. For extramarital adultery, pelting with stones to death is prescribed (Refer Page No.7, Center on Juvenile and Criminal Justice).