To attempt repairs on paper punches which won't come free using the methods in step one, you may have to take the paper punch apart. To do this, carefully check around the edges of the punch where the plastic cover meets the metal base. Usually you will be able to see a small metal tab. This tab helps to hold the metal base to the cover.
Wearing eye protection in case the spring explodes from your punch, carefully use a fine bladed screwdriver to pry the plastic cover gently away from the base at the area of the tab. You shouldn't have to exert a lot of force. If you get the right point on your plastic cover, the cover will pop off easily.