The difficulty you may experience is due to you both being owners and having a joint mortgage on the property, your Mortgage provider will not care who pays the mortgage as long as it is paid, and they can pursue you or your ex partner for the full amount (not 50%). If your ex-partner agreed to be removed, the mortgage provider may object, as they would no longer be able to pursue her if mortgage payments were not received.
Your ex-partner may not be aware she would be liable for the mortgage payments if something were to stop you paying and may agree to co-operate. You then need to prove to the mortgage provider that you are able to pay the mortgage on your own, particularly if the property were rented, but do remember you would be taxed on any profit you made and may be liable for CGT when the property were sold.