Lay blankets on the floor in front of the sliding glass door to protect it. If you have multiple blankets, use them to help you slide the door panels along the floor instead of carrying them.
Insert a pry bar between the wall and the interior trim. Pull the trim away from the wall and set it aside. Go outside and cut along the caulk line where the trim meets the brick wall, using a utility knife. Insert the pry bar behind the trim and pull it away from the wall. Set it aside.
Remove the sliding screen door by lifting its bottom edge out from the sliding track and pulling it toward you. Lower the screen door so the top edge is freed from the upper track, and set the screen aside.
Open the sliding glass door. Insert a small screwdriver into the wheel's adjustment screw hole on the edge. Turn the screwdriver to the left to lower the wheel height and free the door from the track. Remove the sliding glass door the same way you removed the screen door.
Back out all the screws that secure the fixed door to the frame, using a drill and Phillips drill bit. Some doors may also have brackets near their top and bottom corners. Remove the screws holding the brackets to the door. Slide the fixed door down to the center of the opening and remove it the same way you removed the screen door.
Insert a reciprocating saw blade between the sliding door frame and the rough opening. Cut through all the screws securing the two slides in place. Cut through the bottom sill, near the center.
Lift up the sill in the center near the cut, and pull it out from underneath the frame's side piece. Repeat with the sill's other half. Pull the remaining portion of the frame out of the opening, toward the exterior.