The 322nd prohibition is that we [i.e. the Beth Din] are forbidden from inflicting punishment upon transgressors and carrying out judgments on Shabbos.

The source of this commandment is G‑d's statement1 (exalted be He), "Do not burn any fire [wherever you may live on the Shabbos day]."

The meaning of this is, "Do not burn someone who has been convicted and condemned to execution by s'reifa (burning).2" This applies to the other methods of execution as well.3

The Mechilta4 says as follows: "[The verse says,] 'do not burn any fire'; but the act of making a fire is already prohibited5! However, it is mentioned separately to teach us a different law — that just as burning is distinctive in that [in spite of the fact that] it is one of the types of judicial execution and [therefore a mitzvah,6 but nevertheless it] does not override the prohibition of Shabbos, so too the other forms of execution do not override Shabbos."

The Gemara7 says that making a fire "l'lav yotzas"8 [it is singled out because it is "only" a regular prohibition]. However, this opinion is not accepted as the final halachah9. Rather, the Gemara concludes l'chalek yotzas [it is singled out to show that each melachah is treated separately], and therefore one must bring an offering for every single melachah which was performed, as explained there.10

[Therefore, according to the Gemara's conclusion, there is no particular prohibition in this verse and it can be used to teach us this prohibition of inflicting punishment on Shabbos.

The Rambam now brings a source which extends the prohibition to all kinds of judicial punishment11]

The Jerusalem Talmud12 quotes [the end of the verse, " 'Do not burn fire] wherever you may live.' Rav Ilah quotes Rav Yanai as saying that we learn from this verse that a beth din is not allowed to judge on Shabbos."13