31 Ἐρρέθη δέ· ὃς ἂν ἀπολύσῃ τὴν γυναῖκα αὐτοῦ, δότω αὐτῇ ἀποστάσιον. 32 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ ἀπολύων τὴν γυναῖκα αὐτοῦ παρεκτὸς λόγου πορνείας ποιεῖ αὐτὴν μοιχευθῆναι, καὶ ὃς ἐὰν ἀπολελυμένην γαμήσῃ, μοιχᾶται.
31 Now, it was said, “If any should divorce his wife, let him give her a certificate of divorce. 32 Now, I am telling you that anybody who divorces his wife, except in a matter of fornication, makes her to be an adulteress and if any should marry a woman who has acquired a divorce, he is made to commit adultery.
This, in many ways, is pretty weird. But here are my thoughts in list format:
- Jesus’ point seems to be that a man who puts his wife into an economic hard spot by divorcing her (putting her away from his household) has not dissolved the marriage covenant on a theological level. But, the man who put her away is held morally responsible for the ‘adultery’ committed by her and the man to whom she becomes married if such a remarriage occurs. This is in keeping with Jesus’ teachings on adultery in 5:27-30 (see my thoughts on that here).
- I follow Glen Stassen and take the Sermon on the Mount to be organized into several triads from 5:21-7:11. The third element of the triad is missing here. But I think that the implication is no different from Jesus’ instructions in Matthew 5:21-26, “Go be reconciled to a spouse with whom you would rather not live.”
- “if any should marry a woman who had acquired a divorce” is Jesus applying the principle to women who have gotten divorced without the proper exception (the matter of fornication). Mark’s gospel references women having the capability of acquiring a divorce in the ancient world in chapter 10:12. In this case, a woman who remarries after acquiring an immoral divorce is responsible for the adultery committed by the man she later marries (he’s not culpable, he can’t be…he didn’t damage the first marriage).
- That being said, Paul reflects on Jesus’ teachings here in 1 Corinthians 7 and he notes that while one ought not leave their spouse, if their spouse leaves them, they are free (in context, free to remarry). One is not obligated to be reconciled to somebody who is actively being unfaithful to their marriage vows by literally living as though unmarried to them.
- It is worth noting that “except in a matter of fornication” probably carries a wider connotation than the words denote. The idea appears to be anything the breaks the commitment to monogamy made in the marriage vows (adultery, leaving, and probably extensible to physical abuse). Jesus is disagreeing with a school of Rabbis who claimed that divorce could occur for any reason including finding a prettier woman to marry.
- It would seem that the “greater righteousness (Matthew 5:19-20)” Jesus is talking about here includes the virtues of interpersonal fidelity and reflexive reconciliation (I made the name of that virtue up, but I’m sure it’s a real one).
Translating ἀπολελυμένην as “a woman who has acquired a divorce” makes the most sense to me. I’m only aware of one scholar who reads it this way (John Nolland), but I’m pretty sure he’s right.
I also got the idea for point 1 above from the passive tense in “to commit adultery.” The idea is that the divorcer is morally culpable for the negative consequences faced by the divorcee. This is also the case for the man who marries a woman who acquires a divorce, he is “made to commit adultery.”
 Kurt Aland et al., Novum Testamentum Graece, 28th Edition. (Stuttgart: Deutsche Bibelgesellschaft, 2012), Mt 5:31–32.
 Glen H. Stassen, “The Fourteen Triads of the Sermon on the Mount (Matthew 5:21–7:12),” ed. Gail R. O’Day, Journal of Biblical Literature 122 (2003): 267.
 Nolland John, “Preface,” in The Gospel of Matthew: A Commentary on the Greek Text, New International Greek Testament Commentary (Grand Rapids, MI; Carlisle: W.B. Eerdmans; Paternoster Press, 2005), 246.