There are several studies investigating the feasibility of basalt powder as a precursor in alkali-activated cement production. The originality of this research lies in investigating the mechanical and durability features of alkali-activated mortars manufactured by partially substituting granulated blast furnace slag (GBFS) with waste basalt powder (WBP). In this study, 20% of GBFS was replaced with WBP, and high temperature (300 °C, 600 °C, and 900 °C) and magnesium sulfate (5% concentration) resistance of the manufactured mortars were investigated. The deteriorations of the mortars subjected to high temperature and magnesium sulfate were examined by compressive strength test, ultrasonic pulse velocity test, scanning electron microscopy analysis, and Fourier transform infrared spectroscopy analysis. The compressive strength of the mortar produced with 20% WBP substitution was 9.9% lower compared to the mortar containing 100% GBFS as the precursor. However, the performance of alkali-activated slag (AAS), known for its good resistance to high temperatures, did not decrease with the WBP substitution. The reduction in strength of both mortars after 900 °C was approximately 86%. No excessive changes were observed in the visual appearance and the compressive strength of the mortars after 3 months of exposure to magnesium sulfate. Microstructure analyses also revealed that WBP substitution had a limited effect on the high temperature and sulfate resistance of AAS.