Giving up parental rights

I have a question about parental rights, or rather giving them up. I have a 14 year old daughter who lives with me, her father is in another state, and I am remarried.

Recently he got upset with her, and stated that he was going to give up “sign off” his parental rights, to not see her or have any contact or relationship with her anymore. I do not believe that a parent can do this (unless adoption is to take place), but he disagrees.

So my question is, can a parent just sign off their parental rights, just because they want to, even though the other parent will not agree to it?