Cats are predatory carnivores. This means that for cats, hunting is a basic instinct. This is despite the fact that you feed her good diet, her 10 000 year old pre-domesticated natural instinct will kick in.
Remember, hundreds of years ago when cats were first domesticated, it was for the sole purpose of keeping grain free of mice and rats and their diseases. This has never left their systems, and even though humans may deem these acts as cruel, they are perfectly natural.
Cats will tire their prey out by chasing after it and playing with it. This way they can kill their pray with minimal harm to themselves.