Can a 14 year old date a 17 year old girl in NM?

It depends on what you mean by, "be with someone." If in a sexual relationship, the answer is no. The age of consent in New Mexico is 17 according to Avert. Living with someone outside your parents or guardian is still a no. The age of emancipation is 18 years or age, unless by court order or married (need parental permission), or military which you not not old enough for anyway.