Machine tools for processing plate-like workpieces by punching include a punching tool including a punch and a punching die, a drive unit for moving the punch and the punching die relative to each other along a stroke axis for cutting a workpiece part free from a plate-like workpiece, a hold-down device that is movable along the stroke axis and that includes a stripper that contacts an upper surface of the plate-like workpiece while the plate-like workpiece is punched through by the punch, a detection device for detecting a reference position of the hold-down device along the stroke axis, wherein the stripper contacts the upper surface of the workpiece at the reference position, and a numerical control unit for positioning the stripper at a particular distance from the reference position such that a workpiece part that has been cut off can be moved away from a processing region.