Two names on deed and only one on mortgage. Can I foreclose if the other person is no longer living here?

Whether one whose name is on the deed is living there or not is not particularly relevant.  But your question indicates a few possibilities with different implications.  If a married couple owned the property at the time the mortgage was signed and only signed the mortgage, the mortgage most likely would be invalid. There might be grounds for reformation but that is not a given. If multiple people not married to each other owned the property at that time and not all signed the mortgage, the mortgage may be valid against the partial interest in the property owned by those who signed so foreclosing could lead to you being a tenant in common with the others.  That could be subject to a survivorship interest if the owners held title as joint tenants with full rights of survivorship, but the survivorship interest would not apply if they were tenants in common or joint tenants.   Another common scenario would be that only one held title at the time the mortgage was sigend and then, after that, transferred title to him/herself and another, the mortgage could be valid against both owners and you would forclose against the full title of the property and get full title to the property upon the expiration of the redemption period. This is the most likely scenario. You would also be able to pursue a personal claim against all who signed the promissory note, regardless whether they all still own an interest in the property or live there.