This study investigates the effects of two different Blaine fineness and three distinct curing conditions on the physico-mechanical properties of a geopolymer-ground granulated blast furnace slag (GGBFS) binder mortar activated through a combination of NaOH/NaS alkalis. By ensuring constant curing and mixing conditions, geopolymer mortar (GPM) specimens were prepared and evaluated to determine their capillary water sorption, capillarity coefficient, and change in unit weight, alongside their compressive strength and flexural strength 3, 7, 28, and 56 d after production. It was found that the capillary water sorption decreased by approximately 50% as the curing temperature of the water increased from ambient temperature to 22 °C. The coefficient of capillarity remained constant across the geopolymer materials, irrespective of the Blaine fineness of the GGBFS. Furthermore, the increase in the unit weight, owing to the variation in the Blaine fineness of GGBFS, results in a reduction in the water sorption properties of GPMs. The GGBFS and alkali-based binders imparted a continuous increase in the compressive and flexural strengths. The results revealed that a Blaine fineness of 6000 cm2/g in the GGBFS under water-curing conditions imparted the most significant advantageous effect on the physico-mechanical properties of a GGBFS binder mortar activated through a combination of NaOH/NaS alkalis.