The Torah in Parashat Vayakhel (35:3) issues the prohibition against kindling a flame on Shabbat, and the Gemara (Yevamot 6b), surprisingly, interprets this verse as referring to execution. Namely, the Torah here forbids Beit Din from killing on Shabbat an offender convicted of a violation punishable by sereifa (burning), thus establishing that no punishment may be administered on Shabbat. The Sefer Ha-chinukh (114) explains that God designated Shabbat as a day of rest for all, even for sinners, and so the Torah forbids punishing sinners on this day.
We might also suggest a slightly different approach. One of the primary themes of Shabbat is contentment. Creative work and pursuing a livelihood are forbidden on Shabbat because we are to feel on Shabbat as though we have everything we need, and that we do not need to work to obtain or produce more. For the same reason, we are required to indulge and enjoy our blessings, to engender a feeling of joy and satisfaction so that we recognize and appreciate all what we have, and affirm that the Almighty has given us all that we need. Just as Benei Yisrael were not to leave their camp in the wilderness to search for manna on Shabbat, and had to rest assured that they had already received all that they needed, we, too, are to feel secure and content on Shabbat, confident that God has provided us with everything we require.
The prohibition against punishing criminals should perhaps be understood along similar lines. On Shabbat, we are to recognize only the good in the world, and not the evil. On this day, when we are to engender within ourselves feelings of contentment and appreciation, Beit Din does not concern itself with the sinners and evildoers. Shabbat is the time to celebrate goodness, without worrying about the evil that needs to be eliminated. Just as on Shabbat we must feel no need to work to earn more money, we must similarly feel no need to work to eliminate evil, and should instead feel content and satisfied with the current state of the world.
Numerous sources cite an interpretation explaining this verse – “Do not kindle fire on the day of Shabbat” – as a reference to the “fire” of anger, requiring special care on Shabbat to avoid anger. In light of what we have seen, this requirement flows naturally from the law forbidding administering punishment on Shabbat. On Shabbat, we are to feel perfectly content and satisfied with our lives, such that we have no need to become angry. Anger is the product of dissatisfaction, the way we instinctively respond to undesirable circumstances. On Shabbat, then, the day when we are to feel as though God had granted us everything we need, and that the world and our lives are precisely as they should be, there is no room for anger. We should not feel angry on Shabbat because we should experience genuine happiness and contentment, such that no adversity can rattle us or disturb our sense of inner peace and serenity