To provide a cutting device capable of improving the cutting accuracy without overloading motors on a pressing side and a receiving side, and its control method for automatically cutting a shape steel or a pipe.

A pressing carriage 2 for moving a steel and a stopper carriage 4 for receiving its tip part are arranged on a carry-in conveyor 1 and a carry- out conveyor 3 of a steel W which are provided on the input and output sides of a cutting machine C in a sliding/fixing manner, and both carriages are driven by a drive source such as a servo motor. A pressing member 21 is provided on the advancing side of the pressing carriage through a damper 23 for buffer, a stopper 41 is provided on the receiving side of the stopper carriage through the damper 41 for buffer, and a pressing detecting means 22 and a receiving detecting means are provided on the carriage, the pressing member or the stopper to position the carriage.