The coal rock breaking ability of disc cutters directly affects the construction efficiency and safety of rescue tunnels in collapsed coal rock formations. This paper establishes the plastic constitutive relationship under the Drucker-Prager (D-P) plasticity criterion, builds up a finite-element analysis (FEA) model for the coal rock breaking with a single cutter on Abaqus FEA, and explores the influence laws of different penetrations and cutting velocities on the rock breaking performance of the cutter. The results show that: as the penetration increased from 3.0 mm to 7.0 mm, the mean vertical force of the cutter grew from 16.97 kN to 23.36 kN, and the mean rolling force rose from 1.79 kN to 3.95 kN. The increase of the cutter's vertical force improves the cutting efficiency, but intensifies the vertical impact, which undermines construction safety. As the cutting velocity increased from 0.6 rad/s to 1.5 rad/s, the mean vertical force grew from 15.64 kN to 22.94 kN, and the mean rolling force rose from 1.46 kN to 4.23 kN. With the increase of cutting velocity, the cutting force grew at an increasing speed. The increase of cutting velocity can improve cutting efficiency, but an excessively fast cutting velocity will weaken the stability of the cutting operation, and add to the wear of the tool. The research method provides theoretical supports to the cutterhead design of tunnel boring machine (TBM) and tunnelling control in broken coal rock formation.