The pursuit of ultrasmooth surfaces of polycrystalline materials is of paramount importance for enhancing the functionality of components and devices, particularly in the fields of optics, electronics, and mechanics. This study delves into the formation mechanisms of ultrasmooth surfaces on polycrystalline copper using ultraprecision diamond cutting techniques. Specifically, a crystal plasticity finite element (CPFE) model integrated with the Johnson-Cook failure criterion to simulate the anisotropic cutting process of polycrystalline copper is introduced. The model captures the influence of microstructures, such as grain boundaries (GBs), on the machining characteristics, including machining forces, chip profile, and machined surface quality. CPFE simulations, corroborated by experimental investigations, reveal that the anisotropic plasticity and elastic recovery within grains, which is coupled with GB accommodation, significantly impact the formation of surface steps at GBs during cutting process. The study demonstrates that optimizing cutting parameters, such as the cutting edge radius and misorientation angle of GBs, is crucial for achieving superior surface finish of polycrystalline copper. By adjusting these parameters, an ultrasmooth surface of polycrystalline copper is successfully obtained with a surface roughness less than 1 nm through ultraprecision diamond turning. This work not only advances the understanding of microstructure-dependent machining behaviors in polycrystalline materials but also provides actionable insights for optimizing ultraprecision diamond cutting processes to achieve ultrasmooth surfaces. The findings have broad implications for the manufacturing of high-performance components and devices where surface integrity is critical.