Plasma in the vacuum arc is usually generated by numerous cathode spots on the cathode surface, each of which produces a supersonic plasma jet. This work studies the physical mechanisms of supersonic ion flow in a cathode spot jet of vacuum arc by using a two-dimension magneto-hydro-dynamic numerical model that considers ionization and recombination processes. Simulation results are presented for different currents of the copper cathode spot (I = 3, 4, and 5 A). The results indicate that in the cathode spot region, there are huge electron and ion pressure gradients (1013–1014 Pa/m) in both axial and radial directions, resulting in the rapid expansion of the plasma jet in all directions. The expansion of the plasma jet decreases the ion density rapidly from 1026 m−3 to 1022 m−3, and the ions reach supersonic speed within 0.4 μm from the cathode spot. Moreover, within 0.2 μm from the cathode spot, vaporized copper atoms quickly become completely ionized because of high electron temperature and electron density. Beyond a certain distance from the cathode spot, the recombination and ionization rates of the ions will be insufficient to alter the ion charge state. In most of the region, the average charge state varies from 1.84 to 2.05. Finally, the plasma parameters of the cathode spot jet predicted by the proposed numerical model are consistent with the experimental and theoretical results.