Groundwater seepage has a significant impact on the stability of the slope of the waste dumping site. In order to explore the instability characteristics of the waste dumping site of Zijinshan Gold and Copper Mine under the action of groundwater seepage, this paper uses physical and mechanical property testing, theoretical analysis of groundwater seepage field, and numerical simulation methods to explore and analyze. The results show that: (1) the internal structure of the rock and soil foundation soil of Zijinshan Gold and Copper Mine waste dumping site softens under seepage, the permeability increases, the pore water pressure increases, the friction between particles decreases, the mechanical strength decays significantly, and the strain softening characteristics are obvious. (2) Under the condition of no seepage, the maximum sliding amount of the slope of the waste dump is 7.82 m, and under seepage, the maximum sliding amount is 10.23 m. The development of cracks on the slope of the waste dump is mainly concentrated within 15 m of the slope surface, and they develop and penetrate upwards at an angle of about 45° at the bottom of the slope, forming a relatively complete sliding surface. The sliding surface is approximately “C” shaped, and the instability radiation range and degree are more obvious. Under seepage, the total number of cracks inside the slope increased by 68.29% compared to without seepage. (3) The seepage effect destroys the structural stability of the slope of the waste dump, and the peak of seepage pressure appears at the bottom corner of the slope. When the internal structural planes of the slope weaken and cannot resist the shear stress generated by external forces, the slope of the waste dump experiences sliding instability. (4) The minimum safety factor of the slope of the waste dump in the research area under groundwater seepage conditions is 1.031∼1.104, and the slope of the waste dump is prone to slip. The proposed “anchor net + grouting” anti-seepage and anti-skid scheme has a good control effect on the stability of the waste dump slope under seepage.