Alkali-activated slag cementitious materials (AASCMs) use alkaline activators to activate blast furnace slag and waste slag to replace traditional Portland cement, which can reduce CO2 emissions. An impact resistance test and scanning electron microscopy (SEM) microscopic performance analysis of alkali-activated slag cementitious material specimens with four different steel-fiber contents are performed. The effects of steel-fiber volume content and strain rate on the dynamic elastic modulus Ed, dynamic compressive strength σd, dynamic peak compressive strain εc, and energy absorption of the AASCM-SS are studied. The results indicate that the dynamic elastic modulus Ed, dynamic compressive strength σd, and energy absorption of the AASCM-SS increase with the increase of strain rate, and the dynamic peak compressive strain εc decreases with the increase of strain rate. The dynamic elastic modulus Ed, dynamic compressive strength σd, and dynamic peak compressive strain εc of the SS-AASCM increase first and then decrease with the increase of steel-fiber content. When the steel-fiber content is 0.5%, the σd and εc of the AASCM-SS are the highest, increased by 9.9% and 19.3%. The energy absorption of AASCM-SS increases with the increase of steel-fiber content. A dynamic constitutive model of the FR-AASCM considering the influence of damage, strain rate, and steel-fiber volume fraction is established. The proposed constitutive model is in acceptable agreement with the experimental AASCM-SS dynamic stress–strain curve, and the correlation coefficient is 0.91.