In this paper, the influence of NaCl freeze-thaw (F-T) cycles and dry-wet (D-W) alternations on the flexural, compressive and bonding strengths of alkali-activated fly ash (FA) and a blast furnace slag powder (BFS) is investigated. The considered NaCl concentration is 3%. The effect of polypropylene fibers on the mechanical strengths is also examined. Scanning electron microscopy (SEM), thermogravimetry (TG) and X-ray diffraction (XRD) are selected to discern the mechanisms underpinning the NaCl-induced erosion. The obtained results indicate that the best results in terms of material resistance are obtained with admixtures containing 60% BFS and 40% FA in terms of mass ratio and 3% polypropylene fibers in terms of volume ratio. The maximum rates of decrease of the flexural, compressive and bonding strengths after 300 NaCl F-T cycles are 21.5%, 20.3% and 22.6%, respectively. The corresponding rates of decrease due to NaCl D-W alternations are 28.1%, 26.1% and 31.5%, respectively. The TG curves show that the alkali-activating activity of BFS is higher than that of FA. Moreover, in the first case, the microstructure of the hydration products is more compact. The results also show that NaCl F-T cycles lead to increasing cracks in the alkali-activated BFS.