Ultra-precision diamond cutting is a promising machining technique for realizing ultra-smooth surface of different kinds of materials. While fundamental understanding of the impact of workpiece material properties on cutting mechanisms is crucial for promoting the capability of the machining technique, numerical simulation methods at different length and time scales act as important supplements to experimental investigations. In this work, we present a compact review on recent advancements in the numerical simulations of material-oriented diamond cutting, in which representative machining phenomena are systematically summarized and discussed by multiscale simulations such as molecular dynamics simulation and finite element simulation: the anisotropy cutting behavior of polycrystalline material, the thermos-mechanical coupling tool-chip friction states, the synergetic cutting responses of individual phase in composite materials, and the impact of various external energetic fields on cutting processes. In particular, the novel physics-based numerical models, which involve the high precision constitutive law associated with heterogeneous deformation behavior, the thermo-mechanical coupling algorithm associated with tool-chip friction, the configurations of individual phases in line with real microstructural characteristics of composite materials, and the integration of external energetic fields into cutting models, are highlighted. Finally, insights into the future development of advanced numerical simulation techniques for diamond cutting of advanced structured materials are also provided. The aspects reported in this review present guidelines for the numerical simulations of ultra-precision mechanical machining responses for a variety of materials.