The alkali-silica reaction (ASR) in granite mechanically produced sand concrete weakens its durability and service life. The effects of different mineral admixtures in inhibiting this reaction are still unclear. Therefore, this study analyzed the inhibiting effects of fly ash, silica fume, and slag on ASR in mortar and conducted engineering tests to validate the effects of these mineral admixtures on suppressing ASR in granite mechanically produced sand concrete. The study shows that as the curing age increases, the expansion rate of granite mechanically produced sand concrete with different dosages of fly ash, silica fume, and slag all increase continuously. However, the higher the dosage, the lower the expansion rate. The optimal dosage of fly ash, silica fume, and slag for suppressing ASR in granite mechanically produced sand concrete were found to be 30%, 20%, and 5%, respectively. However, under long-term conditions, there is still a risk of expansion, necessitating increased dosages or the combined use of mineral admixtures (e.g., fly ash and slag) to enhance synergistic inhibition effects. Engineering applications show that granite mechanically produced sand concrete with mineral admixtures still exhibits good durability even under long-term traffic-induced loading conditions. The results of this study can serve as a theoretical and data reference for the inspection, construction management, and operational maintenance of granite manufactured sand concrete pavement.