This paper presents analysis of mechanics in a micro-cutting process of a single-crystal metal mechanisms of deformation and material removal related to an anisotropic crystallographic structure of a work-piece. A crystal plasticity theory was implemented in a finite-element (FE) modelling scheme to consider inherently anisotropic deformation of a single-crystal metal at micro-scale. A new shear-strain-based criterion and several conventional strain-based criteria were employed to simulate the material removal process, and their effect on the anisotropy of cutting forces was studied. Subsequently, the micro-cutting process of single-crystal copper was predicted using FE modelling by combining the crystal-plasticity theory and the proposed criterion of material removal. The validity of the present FE modelling methodology was corroborated through a comprehensive comparison between FE simulations and experimental data in terms of cutting forces, chip morphology, deformation field, pile-up patterns and misorientation angle in the work-piece.