A plate material cutting unit is equipped with: support devices for supporting the lower edge of an upright plate material; fluid guides for applying fluid pressure on a surface of the plate material which is held upright on the support devices, to support the plate material in a non-contact manner; a scribe forming device, equipped with a scribing blade for forming a scribe for cutting on the plate material, by moving along the surface of the plate material, which is supported by the fluid guides; a clamp, for gripping a portion of the plate material adjacent to the movement trajectory of the scribing blade along the plate material; and a cutting device, equipped with a pressing member for pressing a portion of the plate material opposite the scribe in a planar direction with respect to the portion of the plate material which is gripped by the clamp.