Hi, Cory! Congratulations on buying your parents home!
Yes, the mortgage needs to be paid off prior to a title transfer. If you have the cash to do this, then you would request a "Payoff" from the mortgage company. Don't assume the amount you see on the mortgage statement is the total due, as there is daily interest, as well as other fees to close out a mortgage account. Once you pay off the mortgage, you want to ensure that the mortgage company releases the lien on the property, and files a "Release" with the County Title records. You can then process a title change with the County.
If you are going to be taking a loan to pay off the existing mortgage, then you would need an escrow period while the new loan is processed.
Please reach out to me if you need any further information!