Divorce in New Mexico

When one spouse wants to end a marriage but the other spouse does not, a divorce may still be obtained (even if that spouse resides in a foreign country). The fact is that when a spouse refuses to sign divorce papers, this will delay things it but it will not stop them. The remedy in such a situation is a "divorce by default". The "petititoner" (i.e. the spouse seeking to divorce) must file a petition in their state court. Then the petition must served on the "respondent" (i.e. the non-filing spouse). When a respondent who lives out of the country that are certain notice requirements that must be met (each state has it own procedures). As a general rule, the respondent has 20-30 days to provide their response (i.e. "answer"). If they fails to do so withing the specified time allowed, then the petitioner may file a notice of "default" with the court.
A copy of the petitioner's application for a default must be served on the respondent (again, special notice provisions apply to an a respondent living outside of the U.S.). After the default notice has been served, the respondent has several weeks has to file a response. If they do not (at least by the deadline given), the petitioner then goes to court for a judge to make a decision as to whether or not to grant the divorce. They will base their ruling solely on the evidence presented by the petitioner. Typically, a divorce will be granted on the terms that the petitioner requested. The respondent does has the right to ask the court to "vacate" (i.e. undo) its order but there are a strict requirements for doing so and if the requirements are not met the decree will stand.
At this point, you are advised to contact a divorce attorney and consult with them directly. These type divorces can get complicated, especially with making sure that proper notice requirements for someone living in a foreign country are met.