I don't want my mother in my life. She is nothing to me can I divorce her or take her name off my birth certificate.

"Divorce" is not the right word - divorce has to do with dissolving marriages, not family relationships.

I am going to assume that you have not yet reached the age of majority in your state. Are your parents divorced, and are you looking to move out of your mom's home and in with your dad? Or are you hoping to go out and live on your own? Depending on your age and circumstance it may be possible to have a court declare you "emancipated" from your parents. This typically requires that you petition the court and show that (a) you are financially able to care for yourself - that you have a job and can afford apartment, food, utilities etc on your own, (b) you are emotionally mature enough to make significant life decisions, and (c) that you would be better off being emancipated. Judges don't grant emancipation very often, and there must be extenuating circumstances beyond "I can't stand my mother."

As for changing your name: once you reach age of majority (or are emancipated) you can have your name legally changed. Again, it's done via a court filing.

No you can't take her name off the birth certificate. She was and is your mother. Once you are declared an adult, you can have nothing to do with your mother if you wish, including having your name legally changed

No you can't take her name off the birth certificate. ...

Except that if OP is a minor, and were to be adopted, that might be possible.

You only divorce a person you are married to.

Without being adopted your mother is always on the birth certificate.

Your mother is and always will be your mother, even if you don't like her.

If you are a adult, then never call, and have nothing to do with her.
As a adult, and a older one, I have not used my birth certificate but once ( to get a passport) in 25 or more years, I have one locked in the safe but you never use it normally in real life as adults.