To provide a mechanism for limiting an upper limit position and a lower limit position of an abrasive-disk cutoff machine which effectively cuts off a workpiece material even when an abrasive-disk has become small, and easily adjusts the upper limit position and the lower limit position, and is excellent in the working efficiency.

In the cutoff machine, such as the abrasive-disk cutoff machine, for cutting off the workpiece material by turning the cutoff abrasive-disk, a stopper 7 disposed on a hinge 4 is provided so as to be movable in the vertical direction and to be engaged.