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Microstructural-related deformation behavior leads to anisotropic machining characteristics of polycrystalline materials. In the present work, we develop a crystal plasticity finite element model of ultra-precision diamond cutting of polycrystalline copper, aiming to evaluate the influence of grain boundaries on the correlation between microscopic deformation behavior of the material and macroscopic machining results. The crystal plasticity dealing with the anisotropy of polycrystalline copper is implemented in a user subroutine (UMAT), and an efficient element deletion technique based on the Johnson-Cook damage model is adopted to describe material removal and chip formation. The effectiveness of as-established crystal plasticity finite element model is verified by experiments of nanoindentation, nanoscratching and in-situ diamond microcutting. Subsequent crystal plasticity finite element simulation of diamond cutting across a high angle grain boundary demonstrates significant anisotropic machining characteristics in terms of machined surface quality, chip profile and cutting force, due to heterogeneous plastic deformation behavior in the grain level.