place some paper over it so you don't look at it.
then put your hand in a plastic bag, put the bag over the paper and scoop it up, pulling it inside the bag, then tie the bag and throw it away.
You can do it. Just take a deep breath, grit your teeth and do what I said above.
I have faith it you that you can do it.
BTW, your cat looks at it as a gift to you from him or her. It's what they do to show their appreciation, they share their kill with those they love.