In machining carbon fiber–reinforced polymer (CFRP) materials of different fiber orientations, the uncut material fracture occurs at different chip formation angles owing to either the fiber-dominated failure or matrix failure. For the matrix failure mode, it is found that the cracks in the damaged material can still affect the chip formation by providing additional Coulomb friction on the closed crack surfaces. To investigate the effect of the damage state of the matrix on the chip formation mechanism, this paper proposes a new cutting mechanics model for CFRP, by attributing the increase of the matrix shear strength to the Coulomb friction on the closed fracture surface. The frictional damage of matrix material, including damage initiation, propagation, and complete failure, is considered to provide a physical explanation for the increase of matrix shear strength and prove that the damaged matrix still influences the chip formation after complete failure. The proposed model determines the transition of chip formation mode, the variation of chip formation angle, and the cutting forces with the fiber orientation, considering the friction in the damaged area and the elastic stress in the undamaged area. According to the comparison with the models which do not consider the material damage state and attribute the increase of shear strength to the “internal friction” without a physical explanation, it is found that the proposed frictional damage model is able to capture the matrix failure in chip formation in the fiber orientation of and and explains the change of chip formation mechanism from matrix compression failure to fiber tension failure in the fiber orientation range of . The necessity of considering the friction on the fractured surfaces in the machining process of CFRP is experimentally validated by cutting experiments at various fiber orientations.