I am 14 years old and I know someone who is 23 who is willing to let me move with them. I live in New Mexico and want to move out. What is the youngest I am able to get emacipated and move you. My parents would sign it willingly.

Emancipation means being able to look after yourself completely, so moving in with others won't cut it..

18 is the youngest. To be Emancipated you first have to have a reason, (not just want to) Then you will have to have a job so you can pay all of your living expenses.

Also you failed to note what type of relationship do you have with this adult who will take you in.
Somehow a little voice says boy or girl friend?

First, I wonder if you are being truthful that your parents would agree. If so, then I feel sorry for you for having such uncaring parents. But moving in with a 23 yr old is NOT the answer. That 23 yr old would, most likely be arrested, especially if your relationship became sexual. Any 23 yr old should know better than to become involved with a 14 yr old.

You need to be at least 16. You can find the law here

New Mexico Emancipation Law - YRN

If you go to court (when you reach 16) and tell them that you want to move in with a 25 yr old, I suspect the court will not find it in your best interests to approve it.

Maybe if you tell us more about what is going on we can help further.