The degradation law of the mechanical properties of red sandstone under coupled temperature and dry–wet cycles is investigated. Red sandstone specimens were pretreated with 1, 5, 10 and 15 dry–wet cycles at temperatures of 5 °C, 25 °C, 45 °C and 65 °C, respectively. Uniaxial compression tests were carried out, and the evolution laws of mass loss, longitudinal wave velocity, peak stress and elastic modulus were analyzed. A statistical damage constitutive model for red sandstone was established based on the Weibull distribution and the effective stress principle. The coupling effects of temperature-induced damage, dry–wet cycle damage and loading damage were considered in the proposed model. To overcome the limitation that traditional models cannot accurately describe the initial compaction stage of rock deformation, an exponential compaction function was introduced to modify the model. The rationality of the modified model was verified using experimental data. The results indicate that the mass loss of red sandstone reaches 0.75% after 15 dry–wet cycles at 65 °C, while the longitudinal wave velocity decreases by 17.54%. The maximum degradation rate of peak stress reaches 36.41%. Compared with the condition at 25 °C, the peak stress increases while the elastic modulus decreases at 5 °C. Both the peak stress and elastic modulus decrease at 45 °C and 65 °C. The proposed model can effectively describe the mechanical behavior of red sandstone throughout the entire stress–strain process, and the calculated curves show good agreement with the experimental results.