A method for machining planar workpieces, in particular metal sheets, using a machine tool, - in which an upper tool is positioned, using at least one motorized drive assembly, along an upper positioning axis that runs perpendicular to a vertical axis, the upper tool being movable, using a vertical drive device, along said vertical axis in the direction of a workpiece to be machined using the upper tool and in the opposite direction, - in which a lower tool that is aligned with the upper tool is positioned, using at least one motorized drive assembly, along a lower positioning axis aligned perpendicular to the vertical axis of the upper tool, - in which the upper and lower tools (11, 9) are moved inside the frame interior of a machine frame, - in which the workpiece lies on a workpiece support (28, 29) for machining, - in which a controller is used to control the motorized drive assemblies (17, 26) for the purpose of moving the upper and lower tools (11, 9), and - in which at least one workpiece part is cut from the workpiece, characterized in that - the displacement of the upper tool along the upper positioning axis and the displacement of the lower tool along the lower positioning axis are each controlled independently of one another, - in order to remove the at least one workpiece part cut from the workpiece after the last separating cut, the upper tool is moved outside of a spatial volume which extends above the cut workpiece part and which is defined at least by a predefined part of the base area of the workpiece part in the workpiece plane and part of a perpendicular to the workpiece part extending in the direction of the upper positioning axis, or by a predefined part of the base area and of a region outside the base area of the workpiece part in the workpiece plane and part of a perpendicular to the workpiece part extending in the direction of the upper positioning axis, and - the cut workpiece part is then removed. - in which an upper tool is positioned, using at least one motorized drive assembly, along an upper positioning axis that runs perpendicular to a vertical axis, the upper tool being movable, using a vertical drive device, along said vertical axis in the direction of a workpiece to be machined using the upper tool and in the opposite direction, - in which a lower tool that is aligned with the upper tool is positioned, using at least one motorized drive assembly, along a lower positioning axis aligned perpendicular to the vertical axis of the upper tool, - in which the upper and lower tools (11, 9) are moved inside the frame interior of a machine frame, - in which the workpiece lies on a workpiece support (28, 29) for machining, - in which a controller is used to control the motorized drive assemblies (17, 26) for the purpose of moving the upper and lower tools (11, 9), and - in which at least one workpiece part is cut from the workpiece, characterized in that - the displacement of the upper tool along the upper positioning axis and the displacement of the lower tool along the lower positioning axis are each controlled independently of one another, - in order to remove the at least one workpiece part cut from the workpiece after the last separating cut, the upper tool is moved outside of a spatial volume which extends above the cut workpiece part and which is defined at least by a predefined part of the base area of the workpiece part in the workpiece plane and part of a perpendicular to the workpiece part extending in the direction of the upper positioning axis, or by a predefined part of the base area and of a region outside the base area of the workpiece part in the workpiece plane and part of a perpendicular to the workpiece part extending in the direction of the upper positioning axis, and - the cut workpiece part is then removed.