High-efficiency precision grinding can shorten the machining cycle of aspheric optical elements by a factor of 2–10. To achieve this objective, ultrasonic vibration (UV)–assisted grinding (UVG) has been increasingly applied to manufacture aspheric optics. However, the mechanisms of material removal and surface formation in UV-assisted aspheric grinding of glass ceramics have rarely been studied. Herein, rotary UV-assisted vertical grinding (RUVG) was used to explore the machining mechanism of coaxial curved surfaces. First, RUV-assisted scratch experiments were conducted on aspheric surface of glass ceramics, which exhibited multiple benefits over conventional scratching. These include a reduction in the scratch force by 37.83–44.55% for tangential component and 3.87–28.15% for normal component, an increase in plastic removal length by 43.75%, and an increase in material removal rate by almost a factor of 2. Moreover, grinding marks on the aspheric surface in RUVG were accurately simulated and optimized by adjusting grinding parameters. RUVG experiments were performed to verify the accuracy of grinding texture simulations and investigate the UV effect. The results demonstrate that UV can improve the surface quality of aspheric grinding when compared with conventional vertical grinding. In particular, the total height of the profile of form accuracy and its root mean square were significantly improved by a factor of 3.38–4.54 and 7.15–10.82, respectively, and the surface roughness reduced by 10.03–12.10%. This study provides deeper insight into material removal and surface generation mechanisms for RUVG of aspheric surfaces, and it is thus envisaged that these results will be useful in engineering applications. © 2024, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.