If my mother died and owed on a Visa and MasterCard would I be responsible to pay the debt?

If you are the executor or administrator, and there are assets available to pay these debts, you may be liable if you don't satisfy these claims before making distributions to beneficiaries.

Check the laws in your state as well. Some states creditors may not even have to file a claim if they send a bill while the estate is open and before the deadline to file a claim pasts. Creditor will probably be in contact soon 

You are not responsible unless your name is on the accounts.

BUT, if there is any money assets in the will, the companies do have the right to file a claim for the money.

Good point that shad made. If there are assets left over, creditors would have to be paid before beneficiaries of the estate.

Joint account yes non joint, no. If probate is opened CCTV could file claim against estate

Not under normal circumstances. If it was a joint account then maybe.