|The Hunting Instinct|
Cats are natural hunters, do not scold your cat for hunting, you will never eradicate this behaviour.
Don't assume that your cat is hungry and is hunting for food; domesticated cats will hunt even when fed regularly. Their prey is usually small rodents or birds.
If you do receive a gift from your cat, accept it. If you do not accept it your cat will think that you are not satisfied and may hunt again to try to please you. The gift is meant as a contribution towards the larder, you should dispose of the dead rodent or bird promptly as it may contain disease.
If you rescue an injured bird from your cat, place it in a safe ventilated box. Take it to an Animal Sanctuary as soon as possible. Do not handle the bird unless it is absolutely necessary; it will already be traumatised, handling the bird will make it worse, and leave nursing of injured birds to the experts.
So far I have received two live Voles from my cats, both Voles were unharmed and were returned to the garden unseen by my cats.