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Have it shaved, sterilized, and destroyed.
My cat kills and eats rodents/birds all the time when she's outside. The bad part is that she always throws it all back up. It's not unusual for to take my dog out for a walk and see a tail or some random body part on the porch and then see a pile of puke right next to it. It's disgusting.
True story: One time my goofy cat ate a mouse and puked it up on the front porch without my knowledge. Well, in the early afternoon I hear a knock on the door and I go and see who it is. I open up the door and I see no one there but I look down and see partially digested mouse body parts everywhere. I think to myself "Thank God whoever was here left 'cause that's disgusting". I shut the door, go back inside to find a broom or something to clean up the mess and I hear a knock at the door again. I go open the door and it was my neighbor wanting to borrow some ice.
I must have turned about 10 different shades of red 'cause I had no idea what to say. Here I am with cat puke all over my front porch and my neighbor outside wanting to borrow some ice. I said nothing about "the mess" and ran and got him some ice came back and handed it to him and he high-tailed it out of there (I don't even want to know what he thought while he was standing there).
Once he leaves I shut the door and wait for a while to make sure that he's gone before I go back out to clean up the mess. I eventually go back out and contemplate how I should go about disposing of the puke. I notice that most of it is all over the doormat so I figure I'll just pick it up by the one end, give it a good flip, and the puke should fly off into the bushes. I pick up the one end of the mat and get into position and I flip that thing as hard as I could. Stupid me I flipped too hard and all the puke came back and landed all over me. I had mouse body parts in my hair and all over my clothes, and I can't even describe the stench. The smell was enough to make me want to toss my cookies (well that along with the fur and assorted bits all over my body).
Naturally I freaked out and started frantically waiving my arms trying to get the mouse bits out of my hair and off my clothes. Once I had cleaned myself off to the best of my ability I ran inside, ripped my clothes off and jumped in the shower. Soap never smelled so good.
Moral of the story: Cats are evil and should be destroyed.