Developing sustainable concrete with less ordinary Portland cement is a growing issue in the construction industry. Incorporating industrial by-products (such as fly ash or slag) or municipal solid wastes (such as waste glass or recycled concrete aggregate) into the concrete becomes an effective way to reduce the consumption of natural sources and carbon dioxide emission if a proper mix design is provided. The present study examines the influence of the combined use of off-ASTM Class F fly ash (FFA) and waste limestone powder (LSP) on flowability, compressive strength, and expansion characteristics of mortar mixtures containing waste glass sand (WGS). FFA and LSP were used as cement replacement while WGS was used as partial reactive siliceous river sand replacement. Material variables included different WGS replacement ratios (25%, 50%, and 75%) with river sand, LSP contents (25%, 50%, and 75%), FFA contents (15%, 30%, and 45%), and different combinations of FFA-LSP (15–10%, 15–15%, 15–30%, and 15–35%). It is shown that the single use of FFA or LSP reduces both compressive strength and flowability of mortar mixture as its replacement level increases. However, mixtures combined with FFA and LSP provide higher or comparable strength to the single LSP or FFA mixture. For the expansion characteristics due to alkali-silica reaction, the single-use of more than 30% FFA or 75% LSP has less than 0.1% expansion, which is a non-reactive aggregate criterion based on the C1260/C1567 when the test period is extended to 56 days. Moreover, the combination of FFA and LSP has a considerable reduction in expansion rate compared to the single FFA or LSP mixture.