Cortical bones are semi-brittle and anisotropic, this brings the challenge to suppress vibration and avoid undesired fracture in precise cutting processes in surgeries. In this paper, we proposed a novel analytical model to represent cutting processes of cortical bones, and we used to evaluate cutting forces and fracture toughness, and investigate the formations of chips and cracks under varying bone osteon cutting angles and depths. To validate the proposed model, the experiments are conducted on orthogonal cuttings over cortical bones to investigate the impact of bone osteon cutting angle and depth on cutting force, crack initialization and growth, and fracture toughness of cortical bone microstructure. The experimental results highly agreed with the prediction by the proposed model in sense that (1) curly, serrated, grainy and powdery chips were formed when the cutting angle was set as 0°, 60°, 90°, and 120°, respectively. (2) Bone materials were removed dominantly by shearing at a small depth of cut from 10 to 50 µm, and by a mixture of pealing, shearing, and bending at a large depth of cut over 100 µm at different cutting orientations. Moreover, it was found that a cutting path along the direction of crack initialization and propagation benefited to suppress the fluctuation of cutting force thus reduce the vibration. The presented model has theoretical and practical significance in optimizing cutting tools and operational parameters in surgeries.