Rambam - Sefer HaMitzvos: Negative Mitzvah 322: Negative Mitzvah 322

Negative Mitzvah 322: It is forbidden to administer death penalties on Shabbat
Exodus 35:3 "You shall kindle no fire throughout your settlements on the Sabbath day"

The Beit Din has the authority to punish and even execute, criminals, however, it may not administer the death penalty on Shabbat.

When a parent loves a child, He stoops down to the child, with such love, he leaves his language to speak the language of the child, he leaves his place to play the games of the child, he leaves his entire world and all the maturity he has gained in thirty, forty years or more to become excited, sincerely excited, by those things that excite the child, to react as the child reacts, to live with the child in the child's world with all his being... But he is not a child. He is an adult, even as he plays with the child. Precisely because he is truly an adult, he can allow himself to be a child and remain an adult. G-d feels our pain and our joy. He lives intimately with us in our world. Yet He is infinite, beyond all things -- even as He lives in our world.

From: Bringing Heaven Down to Earth by Tzvi Freeman - tzvif@aol.com