for some reason our mutt cat treats mice like a car. It chases them but does nothing with it (like a dog chasing a car)
This is an example of
neoteny, the retention or resumption of traits normally lost in the transition to adulthood.
Again, to contrast cats with dogs, dogs have been
bred to retain puppy behaviors into adulthood. Wolf puppies bark, wag their tails, chase sticks, wrestle, and enjoy forming rather large groups; but adult wolves lose all of these traits. Adult dogs, on the other hand, continue to behave in these ways until the day they die. It's much of what endears them to us.
Cats have not been selectively bred long enough to make this transition, and the fact that they are not pack-social by instinct gives them a handicap in even starting it. However, when we pick cats up and carry them around, feed them, give them toys, and absolve them of almost all responsibilities except the fun ones like chasing mice, we are essentially treating them the way their mothers treated them when they were babies. This triggers a
neoteny reaction: a reversion to kittenhood and a resumption of kitten psychology.
Kittens who are too young to eat meat nonetheless chase things because it tones their muscles, vision, and paw-to-eye coordination so when they're grown up they will be able to catch their own food. An adult cat who undergoes neoteny does the same thing: chasing mice without (necessarily) eating them.
Our piss-elegant Persian cats would have died before messing up their coiffures by butchering their own meat. When they caught something, they brought it to us to thank us for taking such good care of them.
And of course assuming that we would butcher it and serve it up for breakfast.