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Deformation behavior at grain levels greatly affects the machining characteristics of crystalline materials. In the present work,we investigate the influence of material anisotropy on ultra-precision diamond cutting of single crystalline and polycrystalline copper by experiments and crystal plasticity finite element simulations. Specifically, diamond turning and in situ SEM orthogonal cutting xperiments are carried out to provide direct experimental evidence of the material anisotropy-dependent cutting results in terms of machined surface morphology and chip profile. Corresponding numerical simulations with the analysis of built stress further validate experimental results and reveal the mechanisms governing the material anisotropy influence. The above findings provide insight into the fabrication of ultra-smooth surfaces of polycrystalline metals by ultraprecision diamond turning.