A machine tool is provided for processing a workpiece, e.g., a metal sheet. The machine tool comprises at least one support configured to, in a support position, support a part of the workpiece on an upper surface, the part being completely separated from the workpiece, and a motion unit for moving the support downwards out of the support position into a discharge position located underneath the support. The motion unit is configured to accelerate the support, at least in a region of the part lying thereon, out of the support position along a gravitational direction with an acceleration which is greater than an acceleration of the part in the gravitational direction, and to move the accelerated support into an open position located outside a path of movement of the part at a speed such that the workpiece part attains the discharge position in free fall.