Abstract: A cutting device for tooling sandwich plates has as its cutting tool a cutting chain (5) with cutting elements in the form of chain links (27, 28, 29) and a chain guide as the guide mechanism, wherein the chain links (27, 28, 29), lying one behind the other in their direction of movement (23), can swivel relative to one another on a swivel axis running transverse to their plane of movement and are moved by means of the chain guide in the plane of movement sometimes in a straight line, sometimes in a curve. The chain links (27, 28, 29) also have several cutting teeth (34) lying one behind the other in their direction of movement (23), which project radially on the cutting chain (5) and have cutting edges (335), which run transverse to the plane of movement of the chain links (27, 28, 29), wherein the perpendicular projections of the cutting edges (35) are arranged in the plane of movement at least partially along a line curved radially to the outside.