In this work, we utilize the peridynamics method, known for its advantages in addressing fracture problems, to simulate the three-dimensional rock-cutting process employed by tunnel boring machines (TBMs). The approach decomposes the rolling motion of disc cutters into rotation and advancement, allowing us to separately analyze linear and rotary rolling motions within the computational framework. We introduce a novel contact model designed to exert stable normal contact force and appropriate rolling contact force experienced by the disc cutter as it rolls. Our simulations of linear and rotary cutting tests provide insights into the typical fragmentation patterns of the rock and the dynamic trends of contact forces on the disc cutter. Additionally, we discuss methods to estimate the wear depth and volume on the disc cutter as it operates, enhancing the prediction of cutter lifespan and efficiency. This paper presents a dependable method for analyzing the interaction between the disc cutter and rock during the cutting process.