A band saw with a complex coordination of a tilting motion and a translational motion between the workpiece and the band saw blade, so that a curved cut is made in the workpiece. The geometric parameters of the cut can be continuously adjusted. This makes it possible to optimize a contact length of the saw blade in the workpiece, which is an important factor in the cutting process. It is thus possible to saw workpieces made of stone and similar materials that are typically difficult to cut. The cut and the contact length of the saw blade can be tailored individually to each workpiece to be sawed. Thus, workpieces of different geometrical dimensions and different material properties, in particular with different material hardnesses, can be processed using the band saw according to the invention without having to undertake significant changes.