Slope cutting is becoming more common in engineering construction to obtain a large floor area. Slope cutting disrupts a slope’s inherent stability, causing instability and sliding. To solve the problem of geological disasters caused by artificial slope cutting, Cangxi County is used as an example to analyze the cutting slope and the height of different slope structures in the county, to study the disaster mode and disaster factors caused by slope cutting, and to analyze the influence of slope cutting height and slope cutting gradient on the disaster process. This study demonstrates that the stability of cutting on different types of slopes is weakened to different degrees, with mixed rocky-soil slopes having the strongest resistance to weakening, thick-soil slopes the second strongest, and thin-soil slopes the weakest. Slope cutting is the main factor of disaster, and rainwater infiltration promotes landslide formation. Numerical simulation is employed to determine the proximities of the slope cutting height and slope cutting gradient, and 75% of the critical value is taken as the proposed threshold value of slope cutting. The recommended cut slope threshold value corresponds to the real stable cut slope gradient on site, and the research findings can be used to guide engineering cut slope decisions in Cangxi County and other red-layer areas.