It depends why they don't want you to. I guess you could explain to them that its your hair and you're not doing anything too wild with it - loads of people get pixie cuts and they look pretty great!
How do I convince my parents to let me get a pixie cut?
explain to your mom that's its your hair and it will look cute. It won't be anything crazy just something simple and cute.
Do it without getting permission. They can do nothing after that.