Why won’t she let me have what makes me happy?

Even if it may sound cliche, she's doing it because she loves you. When she hears about you hurting yourself, all she sees is that her child that she loves very dearly is in pain. She may not know what to do to help you with your mental pain, but she does know that she can stop you from inflicting physical pain on yourself, so that's what she does. Maybe you could discuss your anxiety and self harm with her, if you haven't already done so, and the two of you could work out how to best help both of you feel better about the situation?

I'm sorry that things are stressful enough for you to be cutting, and you can message me if you need to. Are you really in control of it, if you have to take razors from a sharpener and hide it? Try to remember that your mom just wants to keep you from injury, or even risk of dying, though she may not understand that this doesn't fix the feelings behind it. There are lots of other ways to exercise control in our lives, like picking a favourite song to listen to, starting a story or picture, or even something as simple as deliberately closing and opening your eyes, or whatever reminds you that your mind and body aren't being coerced, or just going through the motions.