One is forbidden to kill animals on the Sabbath. One who does, in an case, kill an animal violates the Sabbath and is sentenced to death by stoning.

Despite the prohibition on killing living beings on the Sabbath, even bugs, the sages were divided on whether one is permitted to kill a louse. According to the sage R’ Eliezer, one is forbidden to kill it, but according to the rest of the sages one may kill a louse. One of the scholars, Rav Yosef, explained the reason for the disagreement: all the sages agree that one is forbidden to kill or slaughter an animal on the Sabbath. How do the sages know this? This prohibition is not mentioned in the Torah. The sages ruled that any activity which took place to build the Holy Sanctuary in the desert is forbidden on the Sabbath. They needed skins of rams to make dividers, for it is written “[Take] skins of rams…and make Me a sanctuary and I will reside amongst you” (Exodus 25:5-8). They therefore had to slaughter and kill the rams in order to skin them. That is why one is forbidden to kill animals on the Sabbath.

Since the prohibition against killing animals on the Sabbath is learned from the killing of rams, the sages were divided about the louse. The sage who forbade killing a louse on the Sabbath compares the louse to the ram: just as the ram dies and gives up its soul, so, too, the louse dies and gives up its soul. The sages who permit killing the louse on the Sabbath think that the louse is not like the ram: the ram reproduces sexually and the louse does not reproduce sexually, it is created from dust and from sweat. A different sage, Abaye, argued that the words of earlier sages imply that the louse does reproduce sexually. They said, “The holy One, blessed be He, sits and nourishes all animals, from largest to smallest, from the horns of the re’em to lice eggs.” Since the earlier sages use the term “lice eggs,” this implies that lice reproduce sexually and so generate eggs. Were they to reproduce as the first sage stated, from dust and sweat, the lice would need no eggs. They answered him thus: lice are produced from dust, and the term “lice eggs” do not refer to eggs produced by lice, but to a different form of insect called “lice eggs.”
(Babylonian Talmud, Tractate Shabbat 107b)