Same sex marriage is not legal in puerto rico. I'd like to travel to NY from Puerto Rico so we can get married there and then petition her as my spouse. She has a valid colombian passport but her visa expired a few years ago. I'd like to know if she can travel? Can she get caught at a TSA checkpoint? If so, what could happen to her? Will she have an order of deportation? Can we then appeal so we can get married?

Yes she will get caught at a passport checkpoint, she might be turned back and refused entry, AND be flagged on the illegal attempt to enter without a VISA. And marriage doesn't even guarnatee she would be allowed to get a green card. I have seen too many cases where they were refused.

She will need to get a new visa. No she can not travel with out it.