How to not get my mum mad by asking something, please help?!?!??!?!!!!?

If your mum is fine with you dying your hair, then I can't see her having a problem with you cutting it up by a few inches? Try talking to her first, tell her that you have saved up the money yourself and it's something you really want; it's not a good idea to go off and do it without saying so when you know she'll be mad. Talk to her.