The procedure for a capital trial under the Sanhedrin, as preserved in the Mishnah (Sanhedrin 6) and carried forward in the 1901 anthology Hebraic Literature, sounds less like an execution and more like an argument the prosecution is trying to lose.
If the condemned man, on his walk to the stoning ground, suddenly remembered a new point in his defense, he was brought back — once, twice, four or five times over — so long as the new argument carried weight. If any witness produced new evidence, the procession stopped. A herald walked in front of the condemned calling out his name, his father's name, the crime he was convicted of, and the names of the witnesses, and shouting: "If anyone knows something that would clear him, let him come forward now." The whole system was built to make sure no innocent man ever reached the stones.
When the procession was ten cubits from the pit, the condemned was ordered to confess. Every criminal was urged to do this, the Mishnah teaches, because confession secures a portion in the World to Come. We learn this from Joshua's words to Achan, the man who stole from the spoil of Jericho: My son, give, I pray you, glory to the Lord God of Israel, and make confession to Him (Joshua 7:19). Achan answered, Indeed I have sinned (Joshua 7:20). And where do we see that his confession was his atonement? In the very next verse: Why have you troubled us? The Lord shall trouble you this day (Joshua 7:25). This day — only this day, the Rabbis read — not the day to come.
Four cubits from the pit they stripped the condemned of his clothes. A man was covered in front; a woman, in front and behind. So taught Rabbi Yehudah. The other Sages said a man was stoned naked, but never a woman. Even at the last moment of a person's life, dignity was something the court argued over.
The whole procedure, start to finish, is the Rabbinic answer to a question that still haunts every justice system: how do you execute a person and still fear God? The Sanhedrin answered by making execution almost impossible, and making confession the one thing that reached past death.