It may seems gruesome to our delicate sensibilities (certainly mine!) but cats, even domestic ones, love to catch mice: mine occasionally comes home with a ‘present’, and has on occasion actually eaten the poor dead mouse, right there! After, of course, proudly showing me the ‘catch’. (I do feel sorry for the mouse, they are so cute actually).
It’s normal healthy cat behaviour: in fact if your cat does that, you know you have a happy cat! Cats are a godsend for keeping all sorts of unwanted small rodents out of the house and they also catch spiders and insects on occasion. Cats are extremely territorial, which means that by instinct they will defend their territory and they will hunt to food: on the minus side you may have the opportunity to witness (and hear) quite a few cat fights in your garden! Pray and territory go together.