The low rock breaking efficiency of conventional polycrystalline diamond compact (PDC) bits in hard abrasive formations prompts the development of PDC cutting elements from the planar structure to the non-planar structure. As an innovative non-planar cutter, the design and research of the three-ridged diamond element (3-RDE) cutter is still in its infancy, and its rock breaking mechanism and laws are not yet clear. In this paper, a three-dimensional (3D) finite element model of dynamic rock breaking with 3-RDE cutter has been established. The accuracy of the numerical model was verified by experimental data. Then, the difference of rock breaking mechanism between 3-RDE cutter and conventional cutter was studied. The effects of back-rake angle, cutting depth, rotational angle, and rock properties on rock breaking efficiency were also analyzed. The results show that, unlike the conventional PDC shear rock breaking cutter, the 3-RDE cutter breaks rock mainly by crushing and shearing, and the rock breaking efficiency is higher. A small back-rake angle and reasonable cutting depth contribute to improving the rock breaking efficiency; the existence of rotational angle is not conductive to the rock breaking. The field application shows that compared with the conventional cutter, the 3-RDE cutter is easier to penetrate into the formation, and is more stable with less torque required. The research results can be of benefit to the design and manufacture of 3-RDE PDC bits.