If you want to talk about him with your mum you should be able to - say to her that you don't want to get her upset, but remind her that he is your business as well as hers, and that gives you some rights. If he has done wrong to her in the past then she can just divorce him and move on, but whether or not you get in touch with him, he will always be your biological father, and it was her choice to make him that, not yours.
I haven't been in your situation, but I think if I was I wouldn't want to get in touch with him. I would want to find out a bit more about him and his family by chatting with my mum, but I really wouldn't want to go chasing after someone who hadn't bothered with me for 13 years. He hasn't kept up a relationship with you, and so why should you feel like he has any kind of hold over you or claim to you? Biology means nothing - any loser can have sex with a woman and leave a baby behind, but it takes a real man to be a father.
You should wait until you're 18.
What if your dad, after you contact him, suddenly decides he wants to be in your life? What if he sues your mother for custody and drag her through the courts for the next 5 years? It would be hell for her.
When you're 18 your father won't be able to screw with your life or with your mother's life.
If you feel uncomfortable asking your mother, maybe another family member can tell u about him without telling your mom.
wait til your 18 or ask a relative