Apparatus for mutual separation of two workpiece components of a plate-like workpiece, in particular a metal sheet, comprising: - a workpiece support that defines a support plane and, when supporting the two workpiece components intended to be separated from each other, supports said components that mutually overlap perpendicularly to the support plane; - a lifting apparatus (22, 23) which is arranged at one side of the support plane and by means of which one of the workpiece components intended to be separated from each other can be acted upon perpendicularly to the support plane in a lifting direction as a removal component, and - a counter-holder (24, 25) which is arranged at a side of the support plane opposite the side of the lifting apparatus (22, 23) to provide effective support in the lifting direction for the removal component that is acted on by the lifting apparatus (22, 23), and which can be transferred into a fixing state and into a releasing state, the removal component acted on by the lifting apparatus (22, 23) at one side and supported by the counter-holder (24, 25) at the other side being fixed to the counter-holder (24, 25) in the fixing state thereof and being released from the counter-holder (24, 25) in the releasing state thereof and it being possible for said removal component to be moved, by means of the lifting apparatus (22, 23), perpendicularly to the support plane relative to the other workpiece component provided as a remaining component by means of a removal movement in the lifting direction and to thereby be separated from the remaining component, characterised in that the counter-holder (24, 25), at least in the releasing state, forms an abutment for the removal component acted on by the lifting apparatus (22, 23) in the lifting direction, which abutment is rigid in the lifting direction and supports the removal component during the removal movement with an orientation of the removal component parallel to the support plane. - a workpiece support that defines a support plane and, when supporting the two workpiece components intended to be separated from each other, supports said components that mutually overlap perpendicularly to the support plane; - a lifting apparatus (22, 23) which is arranged at one side of the support plane and by means of which one of the workpiece components intended to be separated from each other can be acted upon perpendicularly to the support plane in a lifting direction as a removal component, and - a counter-holder (24, 25) which is arranged at a side of the support plane opposite the side of the lifting apparatus (22, 23) to provide effective support in the lifting direction for the removal component that is acted on by the lifting apparatus (22, 23), and which can be transferred into a fixing state and into a releasing state, the removal component acted on by the lifting apparatus (22, 23) at one side and supported by the counter-holder (24, 25) at the other side being fixed to the counter-holder (24, 25) in the fixing state thereof and being released from the counter-holder (24, 25) in the releasing state thereof and it being possible for said removal component to be moved, by means of the lifting apparatus (22, 23), perpendicularly to the support plane relative to the other workpiece component provided as a remaining component by means of a removal movement in the lifting direction and to thereby be separated from the remaining component,