Recently, interest in astronomy has increased internationally, and the technological development of lenses for large space telescopes is progressing. The multi-order diffractive engineered (MODE) lenses can make a large space telescope light and thin. However, because glass lenses are difficult to machine, we have adopted a method of molding at high temperature and high pressure. The STAVAX is commercially available chrome alloy stainless steel, and it is applied as various mold materials. The ultrasonic vibration cutting was adopted for ultra-precision machining because the tool wear is severe when cutting the STAVAX with a diamond tool. To achieve a flat surface for smooth ultrasonic vibration cutting, we performed a precise shape cutting using a CBN tool and confirmed and observed changes in the surface roughness and hardness depending on the cutting conditions. The ultrasonic vibration cutting was performed on the surface of the machine using a CBN tool, and the surface roughness was observed. It was confirmed that the surface roughness was impacted by the surface hardness. The specimens with low surface hardness showed the highest surface roughness at approximately 3 nm.