Sefer HaChinuch ספר החינוך

The commandment upon the court to stone the one liable: That the court is obligated to pelt with stones one who has transgressed some sins. And one of them is one who has sexual relations with an engaged maiden, as it states (Deuteronomy 22:24), “and you shall stone them with stones.” And this is one of the four well-known death penalties of the court — and they are stoning, burning, killing (beheading) and strangulation. And in Sanhedrin 49b in the chapter [entitled] Arba Mitot, Rabbi Shimon and “our rabbis” disagreed [regarding] which is more severe, stoning or burning. And it is “our rabbis” that said that stoning is more severe. And the matter of stoning is thus (see Mishneh Torah, The Sanhedrin and the Penalties within Their Jurisdiction 15:1): Four ells distant from the house of stoning, we remove the clothes of the man who is obligated in stoning, until he remains naked, and [then] we cover his nakedness in front of him. And a woman is not stoned naked but rather with one garment. And the house of stoning was two stories tall. And he goes up there — [as do] his witnesses — and his hands are tied. And one of the witnesses pushes him on his midriff and he falls to the ground on his heart. And if he does not die from the pushing, the witnesses pick up a stone that was laying there — [weighing] a load for two people — and they release their hands and hurl the stone on his heart. And if he [still] doesn’t die, his stoning is by all of Israel, as it states (Deuteronomy 17:7), “The hand of the witnesses shall be upon him first, etc.”

I have written a little about the roots of the commandment of the four death penalties in the Order of Mishpatim (Sefer HaChinukh 47).

The laws of the commandment — that which they, may their memory be blessed, said (see Mishneh Torah, The Sanhedrin and the Penalties within Their Jurisdiction 14:4) [that] stoning is more severe than burning, and burning than killing, and killing than strangulation; and [that] anyone who is obligated in two death penalties of the court, whether it is from two sins or from one sin, is sentenced to the more severe; and [that] all those who are liable for death penalties that get mixed up, one with the other and we do not recognize them, are all sentenced to the lighter [penalty] among them (see Mishneh Torah, The Sanhedrin and the Penalties within Their Jurisdiction 14:6); [along with] all of the rest of its details — are [all] elucidated in the sixth chapter of Sanhedrin.

And it is practiced at the time of the Temple. And a court that transgressed this, and did not stone one who became obligated in stoning — even if they killed him with a different form of death — has violated this positive commandment.