The study of the mechanical behavior of layered anchored rock is essential for addressing the stability control challenges of surrounding rock of the roadway in layered rock masses. This paper focuses on a novel constant resistance large deformation (CRLD) anchor cable and conducts a comparative study on the uniaxial compressive mechanical behavior of unanchored rock, conventional high-strength (HS) anchor cable, and CRLD anchor cable anchored rock under different bedding dip angles α (30°, 45°, 60°, 75°, and 90°). The strength characteristics, failure characteristics, and acoustic emission characteristics of various specimen types were analyzed with emphasis. The results indicate that with the increase of bedding dip angle, the elastic modulus, peak strength, and residual strength of all specimen types exhibit a trend of decreasing first and then increasing. Compared to unanchored and HS anchored rock, the values of various mechanical parameters for CRLD anchored rock show varying degrees of improvement. The failure modes of various specimen types under different bedding dip angles can be classified into five categories based on the characteristics of the crack distribution. Through comparison, it was found that the CRLD anchor cable can effectively restrict the occurrence of bedding shear failure within the anchored zone in layered rocks with smaller dip angles (30°, 45°). It also transforms the failure mode of layered rocks with larger dip angles (60°, 75°) from a single mode of bedding shear failure to a mixed mode of bedding-bedrock failure. However, under a bedding dip angle of 90°, the two types of anchored rocks exhibit similar failure forms. Comparing the acoustic emission characteristics of the two types of anchored rocks, it is observed that under different bedding dip angles, CRLD anchored rocks exhibit a more uniform distribution of acoustic emission counts, a smoother energy release process, and significantly lower peak count and cumulative energy values. Finally, a numerical model for layered CRLD anchored rocks was constructed based on the discrete element method. The reliability of the experimental results from the physical model in this study was verified by statistically analyzing the quantity evolution process and orientation distribution of microcracks in the numerical model.