I don't really know, because it says the man finds "some uncleanness", which is super-vague. But I know that typically people will say that this is what the pharisees were questioning Jesus about... they were demanding he clarify the grounds for divorce. I can't say I understand what deuteronomy is saying... but Jesus explains that the law was given because of people's hard-heartedness; that I think I understand.
3The Pharisees also came unto him, tempting him, and saying unto him, Is it lawful for a man to put away his wife for every cause?
So, they don't specifically mention divorce here; and Jesus answers thusly:
4And he answered and said unto them, Have ye not read, that he which made them at the beginning made them male and female, 5And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? 6Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder.
Jesus answering in this way; I believe; means that there really should never have been a "putting away" or a divorce.
7They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away?
So, this is why I think people would say the discussion does include divorce. This might just be the pharisees trying to move the goalpost on Jesus- it does say they are testing him- but either way, Jesus answers the question as to the reason for the law:
8He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so.
This verse could probably start some arguments. What is Jesus saying here?
Men had hardened hearts because they would just send their wives away and marry someone else- so this law was made to help women that were being screwed over by their husbands (which might have some support in the prophets).
-or-
People in general had hardened hearts; so this "putting away" (accompanied by divorce in the law) was tolerated: but it was never supposed to be that way- God never intended us to become hard-hearted, and he never intended us to put away or divorce our spouses.
9And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.
This is where I think people would say that Jesus is clarifying what it means to "find some uncleanness"; and he is answering the pharisees original question of putting women away. Perhaps she has committed some sexual immorality- the man knows that she did it, but there are not witnesses enough to stone her, but he can still put her away, and marry another: and that's the only circumstance where it's okay.
But, strictly looking at his words, he never says "divorce", even though in the law the "putting/sending away" goes with the "divorce".
And if Jesus wasn't talking about divorce here, that leaves us with the question 'what qualifies as a legitimate "some uncleanness" in deuteronomy. Surely it doesn't mean that a man can divorce his wife because she is on the rag, or something like that; that would be dumb... I mean... weren't people unclean after they had sex? I'm pretty sure you couldn't just have sex with your wife and be like "ugh.. you're unclean!! get out!!!" That doesn't make sense.