Positive commandment · Mitzvat Aseh #226 of 613
For a court to execute by decapitation
להיות בית דין הורגין בסיף
The verse · Shemot 21:20
וְכִי־יַכֶּה אִישׁ אֶת־עַבְדּוֹ אוֹ אֶת־אֲמָתוֹ בַּשֵּׁבֶט וּמֵת תַּחַת יָדוֹ נָקֹם יִנָּקֵם
“And if a man smite his servant, or his maid, with a rod, and he die under his hand; he shall be surely punished.”
The Rambam’s words
For a court to execute by decapitation, as [Exodus 21:20] states: "Revenge shall surely be taken."
להיות בית דין הורגין בסיף, שנאמר: "נקום, יינקם" (שמות כא,כ).
Why · Sefer HaChinuch #50
The commandment on the court to kill with the sword one who is liable
“It is from the roots of this commandment that G-d wanted to uproot evil-heartedness and severe cruelty from His holy people. And therefore He commanded that anyone, whose great anger overpowers him to the point that he strikes his slave who is in his home and has no savior, should be killed.”
Where in the Mishneh Torah
Hilchot The Sanhedrin and the Penalties within Their Jurisdiction הלכות סנהדרין והעונשין המסורין להם