In order to study the dynamic response characteristic of the rock-breaking process by polycrystalline diamond compact (PDC) bit cutters, a three dimensional numerical model of rock-breaking is set up based on smooth particle hydrodynamic-finite element (SPH-FE) coupling method, and the influence factors are analyzed. Research shows:• the spread of stress wave in rock has obvious local effect and the rock-breaking process has "leap form" characteristic; • cutting force and axial force increase approximate linearly with the increasing of cutting depth;• the increase of cutting speed will accelerate the process of rock-breaking, but has little effect on the cutting force; • the cutting angle is closely related to rock-breaking efficiency, and the optimization of cutting angle depends upon lithology, • the optimum cutting angle of shale, sandstone and granite should be between 3°~7°~-4°~-1° and 1°~5° respectively. Keywords: polycrystalline diamond compact drill bit (PDC drill bit), smoothed particle hydrodynamics-finite element coupling method (SPH-FE) method, crack propagation, rockbreaking efficiency.