PURPOSE: To enable cutting which does not cause any defect in a surface by constructing at least either of upper and lower cutters relatively movable in the direction of the transfer of a slab and parting said slab in its longitudinal direction, by a parting force in the slab transferring direction, at a stage where a thin wall part remains in the body material of said slab.

CONSTITUTION: When a slab body material 1 which is continuously transferred in the direction of arrow A is cut off, an upper and a lower cutter 3, 9 are lowered and raised and brought closer to each other, and the slab body material 1 is constricted with conical recesses, corresponding to the conical sections of the cutters, being formed on the top and bottom surfaces, leaving a thin wall part 1' in the middle part of its thickness. During this time, the slab cutter is moved together with the slab body material 1 in the direction of A. Then, a separator cylinder 17 is operated and the lower cutter 9 is displaced in the A direction, thereby applying a parting force that severs the slab 1" to be separated from the slab body material 1, to the thin wall part 1'. After that, both cutters 3, 9 are retracted in the mutually parting directions while the cylinder 17 is returned, restoring the cutters in their original positions.