The beneficiary is not responsible for the mortgage of the insured person, unless the beneficiary is also named on the mortgage as a mortgagor (Borrower in a mortgage contract who mortgages the property in exchange for a loan).
If the beneficiary is not named on the insured's mortgage as a mortgagor, then the beneficiary would not be responsible for the mortgage loan and debt repayment.
However, you may want to speak with a lawyer about any obligations you may have as a beneficiary of the life insurance policy, including any tax issues related to the life insurance proceeds.