Elliptical vibration cutting is a machining technology that drastically reduces cutting resistance by vibrating the tip of the blade in a circle or an ellipse. The addition of elliptical vibration to the tool means that when chips are produced, they are lifted up by the cutting surface while the machining is performed. This allows a signficant reduction in resistance during cutting. It also makes the practical ultra-precise cutting of high-hardness die steels using diamond bites, which was previously deemed impossible, achievable. A smooth surface finish can be obtained without polishing or plating when elliptical vibration cutting is used.