A cutting device includes a table for placing thereon a workpiece. A tool unit supports a cutting tool and is laterally tiltably supported on the table, so that the rotational axis of the cutting tool can be inclined relative to a horizontal direction. A positioning device includes a first positioning member and a second positioning member that can interact with each other to position the tool unit at a plurality of laterally tilted positions. At least one of the first and second positioning members can be moved to change the laterally tilted position positionable by the positioning device.