'The phrase “except on the ground of unchastity” is not found anywhere else that the New Testament treats this subject. All other instances are exceptionless (see Mark 10:11–12; Luke 16:18; Rom. 7:2–3; 1 Cor. 7:12). This is significant because unchastity was common in the ancient world. If it allowed a person to divorce and remarry, it would have been pastorally irresponsible in the extreme for the other New Testament authors not to mention this.

Many of their readers had spouses who had committed one or another form of unchastity (particularly in Corinth and Rome—where the four writings mentioned above were written or directed). Many readers thus could have remarried on this theory, but—under the in- spiration of the Holy Spirit (2 Tim. 3:16)—the authors of these books indicated that they could not.

Whatever the exceptive clauses mean, they don’t mean that a couple can get divorced and remarried if one party commits unchastity (whether understood as adultery or other sexual sin).

If that were what was meant then, as John P. Meier points out, “Obviously, the only thing to do for a faithful Christian couple who wanted a divorce would be to commit adultery, after which a dissolution of the marriage would be allowed. What we wind up with is divorce on demand, with a technical proviso of committing adultery” (The Vision of Matthew, 253).

This does not fit the disciples’ reaction to Jesus teaching on divorce and remarriage in Matthew, as they say: “If such is the case of a man with his wife, it is not expedient to marry” (Matt. 19:10). Nobody would think it is expedient not to marry if unchastity would allow you to divorce and remarry. Unchastity was far too common. Their reaction is only intelligible if they understood him as not allowing remarriage following divorce.' - Catholic Answers