The red beds that are widely distributed in hilly areas in eastern Sichuan Province are inevitable rock and soil masses in engineering construction. In order to obtain a larger building area, engineering slope cutting is quite common in red bed hilly areas. Engineering slope cutting destroys the inherent stability of a slope and causes geological disasters. In order to practice the concept of sustainable development and explore ways to develop and utilize land resources reasonably and reduce the possibility of geological disasters caused by engineering slope cutting, this paper took the slope cutting sites caused by rural housing construction in the red bed area of Wanyuan City as research objects. The internal and external factors affecting the stability of the cut slopes were summarized through a field investigation, and two typical slopes were selected for analysis. Sampling and indoor tests were conducted to obtain the geotechnical parameters. Geo Studio software (2018 R2) was employed to establish numerical models, simulate the stress and strain distributions, and compute stability coefficients under different slope cutting conditions at the same time. Based on field investigations and numerical simulations, the three main failure modes of shallow landslides caused by slope cutting were summarized, and the evolution process of slope landform accelerated by slope cutting activities was deduced. In an engineering application, the functional relationship between the cutting height and the stability coefficient was fitted. It was found that the critical cut height values of soil slope were 6.3 m, 6.2 m, 5.2 m, and 2.6 m at slope of 10°, 20°, 30° and 40°, respectively; the critical cut height values of rock–soil mixed slope were 9.3 m, 6.5 m, 5.9 m, and 2.2 m at slope of 10°, 20°, 30° and 40°, respectively. The research findings can be used to prevent and manage the hazards caused by slope cutting in this study area.