If I buy a Mint, do I still get to use the coins from the treasures I played that turn to buy a Grand Market?
Just because you trashed the coppers doesn't mean you haven't earned the coins for that turn (and can spend them).  Their value to you is accrued when you play them.

Per the Prosperity rules you must play all treasures you want to use, before you buy cards.  The rules for Mint state:


  If you buy multiple cards in a turn, trash your Treasures right when
  you buy Mint; you still have any leftover coins they produced for spending
  on something else.


So the order would be:


Play 11 coppers
Have 11 coins to spend and 2 buys
Purchase a Mint (have 6 coins left to spend and 1 buy)
Resolve the Mint card and trash all coppers (still have 6 coins and 1 buy to spend)
Purchase Grand Market (valid because no coppers are in play).