According to many (but perhaps not all) Christians and many secular philosophers (and persons of other faiths) marriage is fundamentally based on the vows that persons make to each other. So, for many Christians in the west, the church does not actually marry two persons; the church recognizes and proclaims (and blesses) the marriage. Insofar as "the married man" and his spouse have ended their vow (whether they think of this as breaking the vow or releasing each other from their vow), the marriage has ended, even if it is still a legal matter of divorce. One reason why the state has an interest in the legality of making and ending marriages is to protect persons from harm and insure fair benefits (e.g. see to it that there is proper child support and a fair distribution of property) that might not happen on a voluntary basis. Apart from such a legal matter, however, it sounds to me that the soul of his earlier marriage (so to speak) has been dissolved in virtue of the two of them releasing each other from their marriage vow.
Your mention of a priest and being in Mexico suggests the context of Roman Catholic religious culture. The Roman Catholic Church currently does not approve or recognize divorce, but it does believe that some supposed marriages are not authentic if, for example, one of the couple did not fully intend to keep (or make a solemn) vow. "Marriages" can also be dissolved (or rendered null and void) if they are not consumated or it is consanguinity is discovered (the couple are related, e.g. siblings or first cousins). Still, many other Christian communities (Lutherans, Baptists, Anglicans, Methodists...) recognize divorce as a sad reality and allow for re-marriage. My own view is that "a divorce" can occur once either or both parties divorce themselves after their solemn vow to each other has ended (or is no longer binding). For some Christian churches that recognize divorce (the Eastern Orthodox for example in Greece and Russia), it is still held that one aspect of the original vow is still binding, the vow to love one another. So, the Orthodox (who hold that you can legitimately be divorced up to three times) maintain that formerly married couples should still pray for their former husband or wife for the rest of their lives (assuming this does not impose an undue burden, e.g. the divorce occurs because of some horrific violence).
Anyway, probably more information than you wanted. I wish you the very best during a difficult time.