You can’t stop spammers altogether, as sometimes they are individuals manually filling in your form. You could at least ban their IP address. Is all this spam coming from one source?
It will affect anyone else who tries to visit from that IP address. If it is someone doing this from their home, that’s no real problem, but if they are (for argument’s sake) sending out this spam from a university computer, you could theoretically be banning the whole campus. So an IP ban can be a big decision. (I don’t know much about IP addresses, though, so it would be good to get more opinions on this.)