I met a man from cuba, but he's married to a woman who is a citizen , and he's marriage is not working, however, he's has no green card, only a marriage visa. He wants to divorce her, can he still get his green card and have permission to work here while he is divorcing his wife?

Generally no. if he hasn't been to the first interview, then his petition will end when he is divorced.

If you are a USC, he can leave the US and get a K-3 visa and enter the US to marry you and then you petition for him.