Hunting is a very normal, very natural behavior for cats. It’s instinctual. Even cats who are well-fed will hunt and indoor cats will play hunt. Owners of outdoor cats have no doubt been surprised by a dead mouse or other prey at their doorstep. While it may be a bit unappealing, your cat is presenting you with her kill and wants you to congratulate her. Since the hunting instinct is so deeply ingrained in your cat, there is very little point in punishing her or attempting to eliminate this behavior.
If your cat is an outdoor hunter, you can put a bell on her collar which serves to warn potential victims of your cat’s approach. She’ll still be able to enjoy the hunt, she may just be less successful. Also be sure that your cat is regularly checked for worms and treated as necessary. Indoor cats love to hunt as well, and you can fulfill this need by providing your with a variety of toys.