A concave drag bit cutter device and cutting method using such a concave cutter bit are provided which provide substantially increased efficiencies over conventional point attack bits. A number of different cutter bit shapes employing a concave cutting face can be used. The cutter bits are intended to replace the conventional point attack cutter bits and can be used in continuous mining machines, saw blades, auger drills, longwall shearers and the like, in cutting and mining operations.