If only one spouse is listed on mortgage but both are on the title and the spouse on the title dies is the surviving spouse responsible for the mortgage?

No or not directly. The loan was between the borrower and the lender with the property pledged as security. If the surviving tenant doesn't want the note foreclosed and the house auctioned by the lender to pay off the outstanding loan then the surviving tenant needs to take action.

The simple method that will work in many cases is to just make the payments on time. Legally you are not required to do so and the lender might technically have the right to call the loan due if you are not on the loan. If the payments are made on time the lender has little incentive to take action.

Or the property can be sold and the loan paid off. Or the owner can obtain a new loan and pay off the old loan. Or the owner can use savings to pay off the loan.

The loan will have a lien that is attached to the property even after the person dies so something must be done to remove the lien or otherwise address the monthly payments.

The first important factor is that one joint tenant cannot encumber the whole property. They can only encumber their own half interest in the property. Therefore, in the case of a default on a mortgage executed by only one and depending on state laws, the lender could not take possession of the property by foreclosure- only the half interest that was mortgaged. The situation would be handled differently in different states under the lien theory/title theory of mortgages. You need to consult with an attorney in your jurisdiction who is familiar with the laws in your particular state.

Generally: In some states the granting of a mortgage by one joint tenant would break the joint tenancy and the mortgage would survive on a half interest. However, in other states a mortgage doesn't affect the joint tenancy and the right of survivorship remains intact. The results in title theory states can vary. In lien theory states, the mortgage would be extinguished upon the death of the mortgagor and the Survivor would take the property free of the mortgage.