In this paper, a three-dimensional numerical simulation model is established based on smooth particle hydrodynamics (SPH) method. In this model, the dynamic behavior of debris flow is described by using the Bingham fluid model, and the bridge pier is regarded as the terrain condition. The repulsive force at the boundary is introduced to improve the boundary condition. Based on flume experiments, the accumulation processes of debris flow impacting the bridge pier with various viscosities and characteristics of the impact force-time curves are analyzed. The physical models are established, and the simulation of three-dimensional dynamic evolution processes of debris flow impacting the bridge pier with various rheological parameters and weights are realized. Moreover, the simulation results of the accumulation processes of debris flow with various rheological parameters and the impact force-time curves are analyzed. It is found that there are differences between the simulation results and the experimental results of the dynamic evolution processes of low-viscous debris flow impacting the bridge pier. From the view of fluid mechanics, the primary reason lies in the ignorance of the energy dissipation owing to lack of a description of Reynolds stresses caused by turbulence. Besides, the bridge pier safeguard procedures under the impact of debris flow with various viscosities are discussed. This work provides a theoretical support for further optimization of the three-dimensional numerical calculation model of debris flow impacting the bridge pier.