Occurrence of toppling failure has been prominent due to the increasing of infrastructure construction, such as road slopes, dams, and hydroelectric stations. Many scholars have done research on the toppling failure characteristics, but paid less attention to the comparison of numerical simulations and physical models in order to propose reasonable and effective stability control methods. Based on previous tests on physical model and field investigations, a numerical model of an anaclinal slope using the three-dimension distinct element code (3DEC) software has been built to simulate the failure process of the physical model. Based on the prominent mechanical properties of the engineering-scale and model-scale negative Poisson’s ratio (NPR) cables, a numerical simulation model of the NPR cable has been developed. The numerical model has been used to simulate the effects of different types of model-scale cables on controlling the deformation of the anaclinal slope. The numerical results show that standard cables, i.e., Poisson’s ratio (PR) cables, cannot control the large deformations of the slope, and the slope finally fails. On the opposite, NPR cables can absorb the deformation energy and maintain the stable constant resistance force during the tensile process. This thereby allows avoiding tensile breakage of cables under the effect of large deformations of the slope and driving the slope towards a new equilibrium state. Through the comparison between the numerical simulation results and the physical model test results, the accuracy and rationality of the numerical simulations have been proven. The numerical model developed in this study can be used for future research works on the failure mechanism of anaclinal slopes and the control effect of NPR cables. It thereby lays a foundation for applying the NPR cables to control the toppling deformations of similar anaclinal slopes.