Abstract: A method and machine for cutting and removing a workpiece part from a plate-shaped material includes cutting the workpiece part with a beam or jet directed onto the material and separating the workpiece part and material. The workpiece part is removed as a scrap skeleton removal part. The cut-free workpiece part is lifted out of a workpiece supporting plane by a lifting device and removed by a gripping device, or the cut-free workpiece part is removed downwards from the plane through a gap between workpiece supporting surfaces by an ejection device, or gravity removes the cut-free workpiece part downwards through the gap. Before cutting the workpiece part free, a sacrificial part adjoining the workpiece part and partially having a common cutting line with the workpiece part is cut free from the material before cutting the workpiece part free in the material or scrap skeleton.