Wood stove pipes have male and female ends. The male ends of stove pipe sections always point in the direction of the stove. They slide down inside the larger female pipe ends. You can tell the two ends apart, because the male end has many crimped ridges around its circumference. This ensures that the creosote that builds up inside the pipe won't dribble out of the joints between the pipe sections. The pipe that extends from the stove to the chimney usually never exceeds 3 feet but can be made up of several sections of pipe.
Allow the stove to cool off completely. This will ensure no smoke or carbon monoxide interferes with the removal.
Put on a pair of gloves and a dust mask.
Cover the floor around the stove with a sheet of painter's plastic.
Remove the three screws holding the top end of the stove pipe to the chimney flue mount. Use a Phillips or flat screwdriver. Undo the three screws holding the pipe to the top of the stove.
Swivel the stove pipe away from the wall. Allow the pipe section in the stove top to pivot. Lift the entire assembly up and off the stove.
Lay the stove pipe assembly on the painter's plastic. Wrap plastic around the pipe and take it out of the house.
Remove the pipe assembly from the plastic and undo all the screws holding each of the pipe sections together. Twist each piece back and forth until the male and female ends separate.