The safety of rock landscapes in Mount Wuyi is significantly impacted by acid rain and wet-dry cycles. In this paper, the decay characteristics of the physical–mechanical properties of red glutenite were investigated under acidic wet-dry cycles. A systematic approach, including cold field emission scanning electron microscopy (CFE-SEM), image processing techniques, and X-ray diffraction (XRD), was proposed to investigate the damage mechanism of red glutenite under acidic wet-dry cycles. The results indicate that with increasing solution acidity and wet-dry cycles, dry density (DD), longitudinal wave velocity (LWV), uniaxial compressive strength (UCS), and elastic modulus (EM) of red glutenite significantly decrease. Under different acidic conditions, DD, LWV, and UCS exhibit exponential decay with wet-dry cycles, while EM exhibits linear decay. A regression fitting was employed to establish a prediction model for UCS, which exhibited a better capability in predicting the correlation between UCS, pH, and the number of wet-dry cycles. Microscopic comprehensive analysis reveals that the interaction between rock dissolution and desiccation is the primary factor leading to changes in the microstructure and mineral composition of red glutenite, culminating in the decay of its physical–mechanical properties. This study holds significant guidance implications for the preservation of cultural and natural heritage in Mount Wuyi.