I had a cat like that. A big ole Maine Coon, 18 lbs of lean mean killing machine.
When I moved into my house, it was overrun with mice. They would sit on a bar of soap and eat one end while crapping on the other. So I wandered down to the Petco, where a local rescue group was adopting out cats. I looked at the cats on display, and then told the lady I was looking for a good mouser. The lady pointed to a cage that was out of sight beneath a table and said "That's a good cat as long as you don't have any small children".
And he was. He was friendly, but played very rough. Liked to ambush me as I walked around the house, and drew blood several times. He also liked to sit in my lap and get pet.
And he wiped out the mice in the house and started clearing out the yard. Pack rats, Kangaroo Rats, Squirrels, Quail, even the occasional Cottontail. He liked to bring them in the house in the dead of night and play with them, making an awfull racket. So I'd have to get out of bed and put on gloves and catch them myself to stop the noise. The Kangaroo Rats were easy to catch on the linoleum in the kitchen, but almost impossible if they got on the carpet in the living room. The birds would fly around the house and get feathers everywhere.
About three years after he moved in, he had a run in with something in the night. Went missing for two days and came home with a couple of small wounds. So I got two dogs, thinking they would keep the larger predators away. About six months later he met his end, about 20 yards from where the dogs were snoozing on the back porch. Found a lot of fur and a little blood there, and more fur about a hundred yards away. Probably a coyote.
Soon enough the mice moved back into the house. So I got a new cat, but this one stays inside. And I'm thinking about getting getting a bigger dog to protect my border collie and springer spaniel.