The continuous cutting apparatus includes a guide rail (5), an extruder (3) for extruding and moving forward a series of sintered magnet blocks (1) on the guide rail (5), a holder plate (6) for holding the magnet blocks in place, and a plurality of OD blades (2) for cutoff machining the magnet blocks into magnet pieces. The cutting apparatus is capable of continuously cutoff machining magnet blocks each into a multiplicity of magnet pieces of desired shape and/or size, achieving a significant increase in productivity and ensuring efficient production of magnet pieces.