The schist from the Lala Copper Mine in Sichuan, China was taken as the research object. Acid corrosion pretreatment under different pH conditions and numbers of dry-wet cycles was conducted, followed by impact compression tests using an SHPB. The evolution laws of the dynamic mechanical parameters and impact failure modes of the schist were analyzed. Based on the fractal dimension of SEM images, the Weibull statistical damage theory, and the Drucker–Prager strength criterion, a dynamic damage constitutive model for schist under the coupled action of acidic dry-wet cycles and impact loading was established. The results show that, with increasing numbers of dry-wet cycles and decreasing pH of the solution, both the dynamic compressive strength and dynamic elastic modulus of schist continuously decrease. After 20 cycles, under pH conditions of 7, 4.5, and 2.5, the dynamic compressive strength decreases to 183.31, 169.52, and 158.54 MPa, respectively, and the dynamic elastic modulus decreases to 32.95, 32.68, and 26.99 GPa, respectively, indicating that strongly acidic environments significantly accelerate the deterioration of the dynamic mechanical properties of schist. The impact failure mode gradually evolves from a “cross”-shaped central failure to a “V”-shaped composite shear failure and complex fragmentation failure. The constitutive model established based on the fractal dimension of SEM images and the Weibull statistical damage theory can reflect the attenuation trend of the dynamic peak strength of schist after acidic dry-wet cycles. The theoretical peak stress values are in good agreement with the experimental results, with an overall error of less than 15%, providing a reference for predicting the dynamic strength of acid-eroded schist.