Rock cutting is a challenging process. Heavy equipment, large cutting forces, high wear rates and large amounts of required energy are common challenges when cutting rock. Traditionally, rock cutting is based on a linear motion of the cutting tool. However, a significant improvement on the cutting performance is expected when using non-linear cutting techniques. Non-linear cutting can be achieved by using an actuator to create a vibrating or oscillating motion on top of the linear forward motion of the cutting tool. The focus in this paper is on the oscillating undercutting disc cutter. This disc attacks the rock like a chisel or pickpoint, aiming at a cutting process dominated by tensile failures. Although the discrete element method has been successfully used for various rock cutting processes, all these processes are based on linear rock cutting tools and most of these researches are based on 2D simulations. The use of a 3D approach is necessary to enable the simulation of oscillatory rock cutting tools. This paper utilizes discrete element method in 3D to investigate non-linear cutting processes, especially the effects of the design parameters such as frequency, velocity and eccentricity of the cutting tool. To resemble rock-like materials the particles are placed in a dense particle assembly and they are bonded together through perfect brittle elastic bonds. The bonds can fail in shear and in tension, allowing the dominant failure mechanisms, i.e. shear and tensile cracks, to occur. After failure of these bonds, particles can still interact through collisions. The simulation results show the effect of the tested design parameters and are compared with analytical models and actual experiments of oscillating undercutting discs.