No, the mortgage payment does not factor into the income, nor is it deductible as an expense. However, certain deductible expenses are sometimes a component of the mortgage payment (mortgage interest, property taxes, private mortgage insurance).
Mortgage interest will appear on the form 1098 issued to you by your lender, and the other two items may or may not appear on the 1098. If they don't, you'll need to separate these amounts from the mortgage payment and then enter them into TurboTax as rental expenses.
You'll find input boxes for all three expenses in the Rental Expense section.