Abstract: A grinding or polishing apparatus and method for grinding or polishing at least one workpiece, in particular having a ferromagnetic property, by way of barrel finishing, having at least one pot-like treatment container, mounted so as to be able to oscillate, for receiving one or more workpieces and grinding or polishing elements, also having at least one workpiece anchoring device for disposing one or more workpieces within the treatment container and for connecting the workpieces to the treatment container in a releasably secured manner, and also having at least one oscillation exciter, by means of which the treatment container can be oscillated, and in that the workpiece anchoring device comprises at least one switchable clamping plate, in particular at least one clamping plate having one or more permanent electromagnets, which is adapted such that a magnetic field emanating outwardly from a clamping surface of the clamping plate can be selectively activated or deactivated.