Your mom is probably just worried that you're growing up too fast. I was 13 when I started wearing makeup, and even then it was just a little bit of mascara (a little bit- not caked on to the point where it looks all clumpy). I'm 15 now, and my mom is still weird about me wearing makeup. She says that it makes me look grown up- which it does, which is why most girls wear it. I totally respect her when she says that though, because it probably does freak her out a little bit. Make up brings attention to a girl. *cough cough* boys.....
Anyways... but I also understand why you want to wear it. I wanted to wear makeup because it made me more confident in myself and I thought that it made me look prettier. Also, it's fun to experiment with your makeup and hair, etc.
So, if you really want to start wearing makeup, why don't you ask your mom that for your next birthday, both of you can go out and shop for some simple things, like mascara, eyeliner, etc. But make sure you don't push her- if she thinks that a certain mascara that you choose is too dark or whatever, go along with it and don't fight with her or else she might not get you anything. Trust me, I've been there.
I hope that I helped (: I tried my best.