A cylindrical workpiece cutting apparatus is provided with a holder in which a metal made cylindrical workpiece is mounted on an outer periphery of the holder and which is adapted to hold the workpiece over an entire length of the workpiece; annular recesses formed on the outer periphery of the holder at a predetermined interval; a laser outputting part provided at a position opposed to the holder and adapted to output laser beam to the workpiece; and a cover portion provided on surfaces of the annular recesses and adapted to prevent attachment of metal particles which are scattered during cutting the workpiece by the laser beam.