I too had the same problem. They were in the marketplace when I went to sell my crops and started spamming me with obscene messages. I had to keep an eye on their "green" online dot that appears on the "messages" that they sent. I finally got lucky and saw them online and clicked on the little green man in the message to go to their farm. I immediately clicked on their avatar and reported them. Once you do that it will automatically block them from sending any more nasty messages. You won't be able to see them or hear them in the public areas of the game. The only drawback is they can still go to your farm and see what you say (even though you cannot see them), but if your friends are on your farm, they CAN see them and hear them (unless, they too, report them or click "ignore" on their character) I hope this helps. Kind of a hassle trying to catch them on their farm, but well worth it once you do.
I'm so sorry you're having this issue in the game. Here's the official 'report abuse' thread, which gives information on how to deal with this. The main thing is to try and click the avatar and 'report abuse' as not only does this send info about the person and the farm to the developers, but it also means you never 'see' the person in the game again. Good luck.