Cats, being carnivores, will eat most types of meat whether it be cooked or raw chicken, turkey, rabbit, lamb. Cats that have access to outside will often hunt and eat mice, b … irds or other wildlife. Tuna and white fish are also usually accepted quite readily and many owners serve this as a treat. pet cat that has access to outside might hunt and eat small birds, mice, voles and other small wildlife animals. In a domestic setting, there are several types of food cats can be fed, with the three main ones being Raw, Wet (canned) and Dry.