A new mishnah (a tiny one)! One who slaughters an animal on Shabbat or Yom Kippur is liable for a death sentence, but the shechitah itself is kosher. But that would only hold true in the case where nothing could have been done to prepare the same shechitah before Shabbat (at the latest, some time on Friday) -- otherwise, it has to be prepared in advance. Especially if meat were to be given to dogs, for example. But can an animal really be "prepared" in advance? Are they really in the world to serve human beings? The Gemara says that their primary purpose is to live in the world, reproduce, and so on. Also, the rest of the Gemara addresses many different concepts of Shabbat - the first being "nolad" -- that which comes into existence on Shabbat. With application to the juices that emerge from the fruit over Shabbat (grapes, olives, and more). Plus, the concern regarding when animals are in the service of human beings - after shechitah is clear, but when in the decision to slaughter the animal to begin with?