Carbon fiber reinforced polymer composite material exhibits excellent mechanical properties, such as high specific stiffness and strength, which bring its increasing use in aerospace and aircraft structures. Theses structures made of composites are mostly produced in near-net-shape, but machining processes such as drilling are usually inevitable for satisfying dimensional tolerances, functional and assembly requirements. Due to heterogeneous, anisotropic, and trans-scale characteristics of composites, the material removal mechanism of composites by machining is quite different from that of metals, thus the well-developed analytical and numerical methods of metal machining cannot be directly applied for the machining of composites. The present paper studies the particular material removal mechanism of machining composites by a micro-mechanical model, and proposes a prediction model of cutting forces based on a two-parameter elastic foundation beam model. The micro-mechanical model of a representative volume element (RVE) in machining a lamina is established with explicit description of the carbon fiber and the matrix. The fiber in the RVE is subjected to cutting forces, and is supported by the rest of the composite. Thus the deflection of the fiber is constrained by the composite surrounding the fiber, which can be modeled as a beam on an elastic foundation. Analytical expressions are established for evaluating the cutting forces and the debonding between the fiber and the matrix using the micro-mechanical model. Different failure modes of fibers with the constraint effect of the surrounding composite can be recognized from the analytical solutions. The effects of variable depths of cutting, different supporting effects on the material removal are presented in the numerical examples. By revealing the fiber deformation, fiber fracture and debonding between the fiber and the matrix, the material removal mechanism is studied for machining carbon fiber reinforced polymer composite.