Devices for separating two workpiece parts, e.g., metal sheets, from one another are described and include a workpiece mounting, a lifting device arranged on one side of the workpiece mounting, and a counter-holder arranged on the opposite side of the workpiece mounting. The counter-holder can be transferred into a fixing state and into a releasing state. One of the workpiece parts to be separated from one another is provided as a removal part, the other as a remaining part. For separating the two workpiece parts, the removal part, which is acted upon by the lifting device and supported by the counter-holder, can be moved by means of the lifting device perpendicular to the mounting in relation to the remaining part by a removal movement. At least in the releasing state, the counter-holder forms a rigid abutment in the lifting direction for the removal part. The rigid abutment has the effect that the removal part is aligned parallel to the mounting. Machine-based systems include a processing unit for producing two workpiece parts from a sheet-like workpiece and a separating device as described herein. Methods for separating two workpiece parts of a sheet-like workpiece are carried out by means of the devices described herein and can be part of a machine-based process.