Provided is a cutter apparatus for machining a difficult-to-machine material, the cutter apparatus including: a cutting tool body which has a fastening portion formed at a center thereof; one or more cutters which are installed on the cutting tool body, and have superhard insert tips fixed to end portions thereof, respectively; and an angle adjusting unit which is installed in an internal space of the cutters, and adjusts angles of the cutters by spreading or retracting the cutters, so that angles of the cutters may be easily adjusted in accordance with a condition for cutting a difficult-to-machine material, in order to prevent damage to the superhard insert tips when machining a difficult-to-machine material having high hardness and high toughness.