Allow the stove and chimney to completely cool before attempting to disassemble the triple wall stovepipe. Spread newspapers on the floor around the wood stove to protect the floor from soot when removing the stovepipe. Cover any nearby furniture with sheets to protect from soot.
Cut through any high-temperature caulk at the seam between the triple-wall stove pipe and the main stovepipe elbow with a utility knife. Cut the caulk between the elbow and the main stovepipe as well.
Remove the screws securing the triple-wall and main pipes to the elbow with a Phillips screwdriver. Twist the elbow slightly to ensure the caulk is cut through and will not hamper pulling the triple-wall pipe out of the chimney.
Position an extension ladder against the house near the chimney and ask your helper to hold the bottom of the ladder steady as you climb onto the roof. Carry a utility knife, a Phillips screwdriver, a small pry bar and a hammer with you up to the roof.
Remove the screws securing the chimney cap to the top of the chimney, using the Phillips screwdriver, and lift the cap off the chimney. If your triple-wall pipe goes through a masonry chimney, grab the sides of the pipe and pull straight up until the entire pipe is out of the chimney.
Otherwise, loosen the screws securing the top of the storm collar to the triple-wall pipe with the screwdriver if your pipe is not in a masonry chimney. The storm collar is the metal cone flashing that surrounds the triple-wall pipe above the roof line. Lift the triple-wall pipe straight up and out of the roof.