Detach the vent piping from the chimney and appliance, if applicable. Use a screwdriver to remove any metal screws and twist counter-clockwise to disconnect the stovepipe sections.
Remove the support box or wall thimble, using a screwdriver to unscrew the screws. Depending on your type of chimney configuration, the chimney pipes may start at the ceiling support box in the ceiling above the appliance, or they may be secured into the wall thimble and start from an outside wall. Once these components are removed, you can begin dismantling the chimney itself.
Twist to unlock chimney sections up the length of the chimney. If the chimney runs up the side of your house, use a ladder to reach them and remove the wall straps from the wall by loosening the nuts and bolts with a wrench.
Remove the storm collar and extended roof bracket from the top section of the chimney on the roof. Loosen the securing nuts and bolts with a wrench and remove any mounting screws with a screwdriver.
Carefully pry up the shingles around the chimney pipe to remove the roof flashing. If any silicone sealant was applied to your flashing, you may need to use a pry bar to detach it from the roof.
Remove the topmost section of chimney.