An apparatus for cutting a laminated sheet material has a cutter receiving plate and a closure member connected to both ends of the receiving plate, and these are accommodated in a guide groove extending transversely across a supporting surface of a pedestal. A belt is supported on the supporting surface on front and back sides of the guide groove, and belt moving members are disposed on both sides of the belt longitudinally thereof for reciprocating the belt longitudinally. The laminated sheet material is supported on the belt and the belt moving members are moved to transport the belt and the laminated sheet material together in the longitudinal direction, with the stacked sheets and the already cut portions thereof moving along with the belt while carried thereon.