Verify that the arm that contains your paper cutter blade is attached properly to the base. The blade of a paper cutter is attached to an arm that moves up and down when cutting paper. This arm is typically connected to the base of the unit via a series of screws. If these screws are loose, it could cause the paper cutter to operate incorrectly. Use a screwdriver to tighten these screws before continuing.
Take your paper cutter to a professional blade sharpener. Paper cutter blades naturally dull over time, especially if you use them on a frequent basis. Do not sharpen the blades on your own.
Replace your blade altogether. You can only sharpen a paper cutter blade so many times before it begins to work improperly no matter what you do. Check the cutter's manual for specific part numbers that you need to use when ordering replacement parts, like the arm. You can usually contact the manufacturer directly -- this contact information is also in the manual -- and order the appropriate part. When it comes in the mail, use a screwdriver to remove the old arm and replace it with the new arm.
Make sure nothing is caught in the paper cutter. Scraps of shredded paper may get caught between the metal blade and the metal or wooden base of the paper cutter. Open the arm on the paper cutter into the full "up" position and remove any small scraps of paper that may be present. Be mindful of the sharp blade.