When an earthquake and precipitation coincide, there is a considerable increase in the danger of tailing dam instability. This work selects a typical metal mine tailing dam in the Jiaodong area and numerically models the danger of tailing dam instability under the coupling of earthquake and rainfall. The simulation addresses the urgent need for efficient early warning of tailings dam instability under extreme natural conditions. The analysis focuses on the tailing dam’s displacement and instability risk in the event of a strong earthquake, intense rainfall, or a combination of the two. Simulation results show that the middle and upper portions of the accumulation dam exhibit the largest horizontal displacement, with the maximum displacement occurring under rainfall coupling conditions. According to the study, there is a higher risk of dam failure in the upper-middle region of the tailing dam, and in two extremely harsh natural settings, an earthquake will have a more significant effect on the stability of the dam. The study’s findings offer a solid scientific foundation for emergency planning and for monitoring and warning of tailing dams during severe natural disasters.