Based on the excavated slope of a waste incineration power plant in Yuxi, Yunnan Province, China, the finite element strength reduction method was used to investigate the variation rules of the safety factor, displacement, and deformation of the bedding cataclastic rock slope containing multi-muddy interlayers under the different conditions of number of muddy interlayers n, inclination angle θ, cohesion c, and angle of internal friction φ. Moreover, the deformation failure mechanism and stability of bedding cataclastic rock slope containing multi-muddy interlayers were revealed. The results showed that, as n increased, the maximum horizontal displacement of the slope increased, the factor of safety decreased, and the key influence on the stability of the slope was the muddy interlayers through the toe of the slope. As θ increased, the horizontal displacement of the slope first increased, then decreased, and then increased again, the safety factor first decreased, then increased, and then decreased again, and the stability of the upright laminar slope was slightly larger than that of the horizontal laminar slope. When the slope angle β was 45°, with the increase in θ, the failure mechanism of the slope manifested as a compression-shear failure, traction-sliding failure, traction-sliding-bending-shear failure, flexural deformation, and bending-buckling-collapse failure in sequence. As c increased, the slope evolved from traction-sliding failure to traction-sliding-bending-shear failure; the stability of the slope increased as c and φ increased.