She's a cat. Cats hunt.
I'm so sorry that her behaviour upsets you so much, but what can you expect? It's how she's programmed to survive, and the instinct remains even though she's being given lots of yummy food. My attitude is to let them get on with it.
If the bird/mouse is obviously shocked or wounded, there's nothing you can do but walk away and leave your cat to it; however, I have saved mice who seemed fine just after they were caught.
I've had cats who've ripped off feathers, scattering them around; and other cats who've just eaten the bird/whatever in a couple of bites: feathers, beak, everything, then, for the next few days acted like they've had a tonic, feeling very proud of themselves. This is easier for us to bear than the type who just play with the catch.
However they behave re hunting, it's my opinion that if you choose to live with a predator you accept all the "distasteful" behaviour that comes with your kitty; otherwise choose a rabbit.
I don't mean to seem harsh, just calling a spade a spade. I hate bells on cats. I hope the collar is snap-release.