Many factors influence rock breakage during cutting processes, including cutting parameters (attack angle, cutting depth and cutting spacing), rock properties and stress conditions. The influence of confining stress on the linear cutting process is currently not well understood. In this study, a 2D discrete element numerical model is developed utilizing DEM software to simulate the linear cutting process of rock using a conical pick. The model accounts for different levels of confining stress to investigate their effect on the cutting process. The numerical model was first validated to ensure its rationality. Subsequently, the rock breakage process under different confining stresses was analysed by observing variations in cutter force, the development of crack extension, particle displacement, velocity variations, and alterations in internal stress. According to the results, the presence of confining stress facilitated the propagation and expansion of cracks within the original rock, particularly along the region where the free surface was present. Subsequently, during the cutting process under different stress conditions, it was observed that as the confining stress increased, the length of radial crack expansion decreased gradually along the tip of the cutter. Under higher stress conditions, a uniform distribution of mostly tensile cracks appeared inside the rock during the cutting process. Additionally, the regression analyses show that average cutting force and specific energy for rock breakage both exhibit an initial increase, followed by a decrease, with increasing confining stress. This indicates that the rock breakage efficiency was high when the confining stress was low and that a high confining stress can instead improve rock cutting. Through these analyses, insights were gained into the mechanisms underlying rock breakage during the linear cutting process using a conical pick under different levels of confining stress. Ultimately, these findings provide valuable knowledge for predicting and optimizing rock cutting processes under different stress conditions.