Abstract: Parts which cannot fall because of their dimensions through an opening of a lower tool are separated from a workpiece plate in a cutting press with an immovable support, a coordinate table, two lateral workpiece supports movable parallel to the y-axis and a transverse carriage displaceable in the direction of the x-axis and having clamping elements, and with a central workpiece support of a plurality of articulately connected supporting elements displaceable in the direction of the y-axis so that a discharge opening for the separated part of the workpiece plate is openable or closable, in such a manner that first a cutting tool separates a workpiece part so as to retain at least one connecting web between separating edges of the workpiece plate and the workpiece part located transverse to the direction of movement of the central workpiece support, the workpiece plate and workpiece support being positioned by the coordinate table above the discharge opening, and before opening of the discharge opening the conn