Cover the area where you'll be working with drop cloths to catch falling debris.
Unscrew and remove the shutters on the walls covered with veneer.
Remove the grout between the stones in the top two rows on the wall. Use an electric grinding tool or a hammer and mason's chisel to cut through the grout, being careful not to damage the bricks underneath.
Sweep out the dust and debris from between the stones.
Pry the stones away from the wall with the hammer and mason's chisel or a pry bar. If you don't have enough room to fit the pry bar or chisel, cut away the edges of the stone until you can pry it off. Stone veneer is fairly fragile.