Due to the complexity of the composite structure, analyzing the material failure process of carbon fiber reinforced polymers (CFRP) is fairly difficult, particularly for the machining process. Peridynamic theory, a new branch of solid mechanics, is a useful tool for dealing with discontinuities. This study presents an ordinary state-based peridynamic (OSB-PD) model for unidirectional CFRP material in the cutting process. In this model, angle tolerance is used to overcome the fiber angle limitation in a classical OSB-PD laminate method, and the short-range force approach is utilized to simulate the contact of the cutting tool and workpiece. The effectiveness of the supplied models is validated by tension and cutting tests. Finally, it can be indicated that the OSB-PD model is capable of predicting machined surface damage and cutting force, based on the comparison of simulation and experimental data.