I am selling my primary residence. I understand the profits are tax free up to 250K/500K (single/married. Is that applied before or after the mortgage is paid off?

[Critter]

The mortgage payoff has NOTHING to do with it.  

The purchase price + cost of purchase + improvements made =  cost basis

Sales price  minus  (Cost basis + cost of sale)  =  Profit 

[tagteam]

"Is that applied before or after the mortgage is paid off?"

The amount of your mortgage is irrelevant.

You calculate your gain by taking your selling price (less selling expenses) and subtracting your cost basis (purchase price) plus improvements.