Can you defer a mortgage payment?
This is going to depend on your lender. And it will also depend on what your definition of "defer" is.
Some lenders have promotions on new mortgages where you don't have to make a payment for the first year (or 6 months, etc..). Of course you'll end up paying them in time.
If your goal is to defer your very first mortgage payment, this sometimes occurs by the simple fact that mortgage lenders set your payment on the 1st day of the month 2 months after the month you sign. In other words, if you sign in August, your first payment would be due on December 1st. If you sign on August 1st, your closing costs would be higher because of prepaid interest, but it would feel like you got to defer a payment because there would be no November payment.
As far as deferring a payment when you already have a mortgage, that's going to depend on the lender. That's what I'm guessing this actual question is about. In this case, you will want to call your mortgage holder and ask them if there are any circumstances where you can defer your payment. Some will have policies set up for hardships, etc... The only real way to answer this question is to call your lender and ask.