Can I use a Judgment order in New Mexico

Not until you domesticate the judgment in New Mexico.  If the original judgment was fully litigated, this should be a fairly simple process which the court clerk can help you with.  If the original judgment was on default, however, you will have to start a new lawsuit in New Mexico in which the initial issue will be whether the California court had jurisdiction over the defendant.  If so, the judgment will be converted into a New Mexico judgment; if not, you will have to litigate the case in New Mexico.