Hi I have a 6 month old baby and the father is leaving to Mexico in a couple of months, I don't want him to have any right over her now that he's leaving. How do I get full custody of my baby, and get him though give up his right.

You can't just have him give up rights.
He is leaving so what rights in specific don't you want him having?

The full custody and be able to travel out of the country without his permission

He can't get full custody
If that is what you are afraid of then maybe you should go file for full/sole custody

Have YOU filed for legal custody yet?

What about child support?

YOU can't take away his parental rights--only a court can do that, and they're reluctant to do so UNLESS the father is a danger to the child AND there is a stepfather to whom you've been married for over a year ready to adopt.

Basically--YOU are ticked off at the father, and YOU want to get even by taking something away from your child.

Pretty selfish, if you ask me.