Abstract: A device for removing pre-cut portions of a material sheet (10) comprising scores or the like. The sheet is placed on the cutting surface (2) of a die (1) so that the pre-cut portion (11) covers an opening (3) in the die (1). The opening (3) in the die (1) comprises at least one recess (4) extending radially towards the axis of the opening (3) and communicating therewith. The recess (4) is shaped in such a way that the head (7A) of a blade (7B) forming a resilient abutment member is retained therein. The blade (7B) yields to the pre-cut portion when a cutting member (12) passing through the opening (3) in the die (1) exerts pressure thereon. The free end of the blade (7B) prevents the discarded portion (11) from returning after each cutting step.