A sorting system and a gripping tool thereof to be mounted on a handling device for handling pieces cut out from planar sheets are disclosed. The gripping tool includes: an engaging head interchangeably paired with an operating end of a displaceable handling device: an actuator mounted on the engaging head, including at least a first actuator unit; and attaching and coupling units having attaching and coupling devices, mounted on the engaging head. The attaching and coupling units are mounted on a frame including at least four rods articulated together through respective hinges arranged on a lying plane. The attaching and coupling devices are arranged on a plane parallel to the lying plane. The articulated frame being supported on the engaging head. The first actuator unit drives at least one of the rods of the articulated frame by rotation around at least one of the hinges on the lying plane.