I've had several cats. I've seen one of them rush out of the house, pounce on a bird, then kill and eat it, even though its food dish was full. Recently, my current cat caught a lizard out back. He wanted to bring it in and use it as a toy, but I wouldn't let him. In about two minutes, there was nothing left but a bit of blood. Tame, mostly-indoor cats know how to hunt, and what to do with their prey. Yes, they do sometimes play with mice until they die (then leave them for you to deal with) but more often than not, they eat what they kill, at least in my experience.