In order to turn a supersmooth surface even if error motions exist on the machine tool, a new single-point machining technology using a flying tool has been proposed. In the process, a discoid slider with a sapphire chip follows the prefinished surface by the action of hydrodynamic bearing. In this paper, the cutting mechanism of the technology was investigated as follows : (1) The height of the cutting edge was kept between the peak and the valley of the surface roughness so that the surface finish was improved due to the truncation. (2) The cutting depth varied following the vertical acceleration of workpiece surface with small delay, which has some possibility of improving the waviness.