Can I go ahead and put my house up for sale if the mortgage is in my name only but the deed also has my spouse's name on it?

If the deed is in both names, you will need to have both people consent to the sale.  Many realtors will require both people to sign the listing agreement.  even though your ex is not on the mortgage, his/her name is on the deed and he/she will need to sign the deed to complete the sale.