Based on the idea of nonlocal theory, peridynamics describes the movement of material particles by solving spatial integral equations. It is suitable for describing the crack growth and fracture behavior of workpiece materials during severe plastic deformation in cutting process. In this paper, the elastoplastic constitutive model of Ti₂AlNb is constructed based on ordinary state-based peridynamics, and material failure and contact criteria are developed. By solving discrete basic motion equations, a state-based peridynamics numerical model is established to study the cutting process of Ti₂AlNb alloy. Then the chip formation process for orthogonal cutting of Ti₂AlNb is simulated and analyzed. The results demonstrate that the peridynamics method can accurately simulate the material deformation and damage evolution during machining of Ti₂AlNb. The error between the predicted chip shear angle of 40.23° and the experimental result of 38.89° is 3.45%. The full width at half maximum of the damage spatial distribution is defined as the width of the primary shear zone, and the predicted value is 0.06 mm with an error of less than 7%.