A self-sharpening refractory metal cutting tool presenting an overhanging cutting portion, i.e. a flange, or ledge, of width equal to (or slightly greater than) the depth of the cut to be taken and maximum thickness equal to tolerable tool flank wear is disclosed. This tool construction has special utility in a novel high-speed cutting method in which only the tool flange does the cutting in which operation the flange is worn away with the wear progressing lengthwise of the flange during which time the flange sequentially performs a roughing cut and then a finishing cut in a single pass.