An experimental study was conducted to investigate the physical and mechanical properties of an intensely weathered mudstone from Northeast China after wetting–drying (W–D), freezing–thawing (F–T), and wetting–drying–freezing–thawing (W–D–F–T) cycles. These cyclic climatic processes have significant effects on the volume, microstructure, stress–strain behaviour, shear strength, electrical resistivity, and P-wave velocity of the samples. The variation in electrical resistivity exhibits an inverse correlation with the volume change, and a strong relationship can be observed between the electrical resistivity and porosity. The cohesion decreases with increasing number of cycles, while the internal friction angle slightly increases; these relationships can be caused by the presence of cracks and large voids and by the increase in the aggregate size and density during the drying and freezing processes, respectively. Moreover, the W–D–F–T cycles have a greater influence on the shear strength than do either the W–D or F–T cycles. This phenomenon is similar to that observed in the P-wave velocity, and the relationships between the shear strength parameters and P-wave velocity are also explored. This study provides nondestructive methods of predicting the deformation and shear strength of mudstones in seasonally frozen regions.