We investigate herein the role of acidic dry-wet cycles and dynamic loading on the mechanical stability of sandstone, which is crucial for managing closed and abandoned mines' safety. Using a split Hopkinson pressure bar, we conducted dynamic compression tests on sandstone samples exposed to four acidic conditions (pH = 3, 5, 6.5, 7) and five dry-wet cycle frequencies (1, 5, 10, 20, 30) at an impact pressure of 0.70 MPa. Our findings reveal that the dynamic stress-strain response of sandstone entails compacting, elastic, plastic, and failure phases, with peak stress and elasticity decreasing as the acidity and cycle frequency increase. Analytical techniques, including EDS, XRD, and NMR, showed changes in composition and porosity, indicating reduced deterioration compared to untreated stone. Based on Weibull distribution and damage mechanics, a dynamic damage constitutive model was developed to accurately predict the sandstone's behavior under these conditions. This model, validated by experimental data, effectively captures the dynamic stress-strain characteristics of sandstone, indicating the importance of understanding environmental degradation effects on rock stability in mining contexts.