A slitting apparatus including a frame, a rotary shaft mounted on the frame, a plurality of laterally stationary circular blades secured to the rotary shaft, and a plurality of laterally movable circular blades movable in the direction along which the stationary blades are disposed and rotatable in slidable contact with the stationary blades so that a sheet passing through between the stationary blades and the movable blades is slit therewith into plural strips each having a width being adjusted by moving the movable blades. A stationary rack extends in parallel with the rotary shaft. A carrier is movable back and forth along the rack. Holders are detachably engageable with the carrier and moved along the rack by the carrier, each of the holders having a positioning rack adapted to project therefrom for meshing with the stationary rack and withdraw thereinto and a movable member for moving one of the movable blades to and withdraw the same from a position in which the movable blade slidably contacts the stationary blades.