I have a mortgage consigned with someone who is divorcing. Only my name is on the deed, can the spouse claim property?

If I am understanding your question correctly, the person who is divorcing is not getting the divorce from you, but from a different person. If that is correct, then the ex-spouse cannot successfully claim any ownership in the property if only your name is on the deed. However, it is unclear why the divorcing person's name was on the mortgage. If they co-signed your debt they would be on the note but not the mortgage. Because you say that they signed the mortgage, it may be that their name was inadvertently added to your deed and that would leave you at risk. Also, if they did co-sign on your debt, that debt could be an issue in the divorce -- not necessarily risking your ownership, but potentially impacting the distribution of marital assets between the two ex-spouses.