In Arizona, can a person that was added onto your home title buy that home from you?

Sure. They can buy your share of the ownership of the property. All you have to do is prepare a deed from yourself, as seller, to that person, as buyer. Then have the deed recorded in the county clerk or county register's office. I suggest that you have this done by a title agency or an attorney to make sure it's done properly. It shouldn't be expensive and you'll know that it was done correctly.