Hydraulic-electric pulsed-discharge (HEPD) rock-breaking technology is a new type of high-efficiency rock-breaking technology that converts electrical energy into mechanical energy of shock waves and has a wide range of potential applications in industrial and civil fields. Due to the difficulty in describing the multi-physical field coupling rock-breaking mechanism involved in HEPD rock-breaking technology, there have been fewer theoretical modeling studies of this technology. In this paper, a multiphysics numerical HEPD simulation model is established, which realizes the whole process of HEPD rock-breaking from the coupling of five fields: electromagnetic field, circuit field, heat transfer field, solid mechanics field, and acoustic field, and combining with two kinds of damage mechanisms. The multiphysics model considers the influence of electrode shape, electrode angle, and electrode spacing on the HEPD rock breaking. From the obtained multi-physics model, it is found that the formation of the breakdown channel is formed by the interconnection of "electrical damage," and the HEPD process is divided into three phases: the formation phase of the breakdown channel, the formation phase of the plasma channel, and the blasting phase of the plasma shock wave. The shock wave causes shear and tensile damage to the rock, but most of the damage to the rock is tensile damage caused by tensile stresses. When electrode bits with tips are used (conical, quadrangular, and pentagonal), plasma channels are more easily generated at the electrode tips. When the electrode angle alpha = 15-30 degrees, the HEPD plays a positive role in rock-breaking, and the maximum penetration depth and the maximum damage depth gradually increase with the increase of the electrode angle; when the electrode angle alpha = 30-45 degrees, ablation is easy to be generated at the insulating medium and the subplasma channel is generated, which makes the efficiency of the HEPD rock-breaking greatly reduced. This paper provides theoretical and technical guidance for developing HEPD rock-breaking technology and drilling tools.