Hi! What happens if I mortgage a home in US and then go through a voluntary deportation? Can I come back to visit my property? Can I sell or rent it?

First, cojnsult with your immigration lawyer. Icannot advise you if you're represnted by an attorney. I can say it would be difficult for you to qualify for a home purchase and mortgage without U.S. permanent residency or citizenship. Next, I am assuming you are in removal/deportation proceedings - you need an attorney who can debrief and brief you in order to answer your Q about returning to USA.