The reason that she does this is she considers you to be part of her pack and is bringing you food as a gift. I read somewhere that it's because she thinks you need help feeding yourself, so she's trying to help you.
Though it's a valid concern, it's actually your cat showing you that she loves you. She clearly did play with them before because she hunts them, and now she's gifting her kill to you.
Make sure when she does this, you don't yell at her or get upset because she's only doing what she's supposed to do and what she finds natural. Otherwise you'll be telling her that you don't accept her love.
Obviously you don't want the mice in your house. I would try taking the dead mouse and putting it on the step directly outside the cat door. If she sees you doing this, she might decide that this is where you plan on having dinner, and she might start leaving them there as well. Make sure she sees you putting them there.
I wonder if a smaller cat door, or one that she has to push with her head a bit harder might dissuade her a bit. That's more a guess than anything though, and really depends on your cat. The idea is that it's more work to get inside than she feels necessary.
The only other option that I can think of is having her not go outside, or at least closing the door and only letting her in and out when you're around. There are so many worries with letting your cat out, and I'm sure you'll find arguments with both sides, but if you want to let her out at her own will, you might have to accept that these things can happen.
I just hope that she hasn't let some live mice in without you noticing yet!
EDIT: Here's an article that gives support to my point about why.
