Sure, the GM can have a goal like Kill the Mice. That's part of the conversation between the GM and players when setting Conflict Goals at the start of the conflict. The players have to agree to the possibility of the GM's goal happening if the GM wins without compromise, just like the GM likewise agrees to the players' goal.
If you lead with a stated goal of Kill the Mice, the players can agree with their own violent goal—and now you're off and running with Death and Killing on the line—or they could back off and say “Whoa, we don't want to fight to the death. How about we try to escape instead?” If they agree that Death is on the line, then they're acknowledging that if they lose (disposition hits 0), they're dead. It's a good idea for the GM to reiterate the risks.
There's always the opportunity for randomness, but you can mitigate some of it with preparation and clever scripting. The mice would do well to be prepared to Fight to kill an animal: have some Fate and Persona handy, be ready to tap Nature, have someone who knows about animals who can test to learn about that animal's weapons (which will help them script when the animal declares what weapon they're using), and have suitable weapons for the patrol. For example, with a Bow, Attack/Attack counts as versus rather than independent.
Even doing everything right, the risk is still there that they could die, but the players will have agreed before they started.
That said, the party can't have a goal to straight up kill the Owl, because the Owl is two levels higher than Mouse on the Natural Order. At best, you could capture, injure, run off using Fighter or Hunger, or otherwise attempt War with Animals using Militarist and Scientist. See the Natural Order section of the book for more details.
Likewise, if the Players' goal is to kill in a Fight—especially a Fight with an animal—it's only fair that the GM's goal is to kill the mice. As a GM, I would not accept their goal without having something equally bad on the line.