In this article, a centrifuge shaking table model test of anchored stabilizing piles for strengthening landslides was established, and the dynamic response characteristics of the pile–anchor–slope under earthquake action were analyzed. On this basis, combined with the fuzzy gray relational analysis and the rank-sum ratio method, the correlation between the amplification of the acceleration response of the heterogenous slope and the dynamic response of the support structure was explored. Based on the obtained results, relevant suggestions for engineering design were proposed. The results showed that the seismic amplification of the complex soil–rock slope reinforced by the pile–anchor structure was not uniform and the amplification coefficient had strong variability. Among them, the amplification coefficient of the slope, dynamic earth pressure, and dynamic bending moment of the pile near the connection of the pile–anchor cable continued to increase; the correlation between the seismic amplification and the seismic behavior of the pile–anchor structure is different at different positions of the slope. The measurement points with a higher comprehensive ranking of correlation are mainly concentrated in the pile–anchor connection, the middle of the slope, and the high-angle soil–rock interface. It is related to the geometric characteristics of the model and the high seismic amplification of the slope; for the pile–anchor connection part and the high-angle soil–rock structure surface of the slope, the shock absorption measures and grouting strength of the anchor cable’s anchoring section should be considered in the engineering design.