Different construction methods have a significant influence on slope stability. Through an indoor model test, two construction methods of cutting a slope, excavation without support and the so-called one-step skip excavation method with the support of antislide piles, were carried out to analyze the mechanical behavior of the slope and antislide piles in the construction. Based on the model test, a numerical simulation was carried out to study the construction stability of the slope and antislide piles during the construction process of the four skip methods (the excavation methods referred to as the two sides followed by the middle part of the slope in parallel, the odd sections followed by even sections of the slope in parallel, the two-step skip in parallel, and the one-step skip). The results show that the constructed antislide piles act as the arch foot of the soil arch effect to restrain the deformation of the soil between piles. By comparing the four skip methods, we found that the ranges of large shear deformation of the cutting slope were roughly the same, and a shear zone was most likely to form in the middle of a slope to be excavated during the construction process of the four methods. The two sides followed by the middle part of the slope in parallel excavation method is more effective than the other three methods in controlling the change of bending moment of the piles and the safety factors of the slope during construction. Thus, this method should be given priority in the actual construction and design of small and medium cutting slopes. The conclusion has specific guiding significance for engineering practice.