This paper presents the influence of supplementary cementitious materials (SCMs), such as fly ash (FA), silica fume (SF), ground granulated blast furnace slag (GGBS), and waste glass fine aggregate (GA), on the alkali-silica reaction (ASR) in high-strength and normal-strength mortar using an accelerated mortar bar test (AMBT). Residual mechanical properties and scanning electron micrographs were used to assess the changes in the matrix. GA reduced the mechanical properties of both normal-strength (NGA_OPC) and high-strength mortars (HGA_OPC), contributing to a decline in overall performance. This phenomenon was a result of the slipping of the GA from the matrix owing to its smooth surface. However, the inclusion of reactive SF and GGBS in the HGA improved the slip phenomenon of the GA, leading to a significant enhancement in its mechanical properties. Following the ASR expansion measurement, HGA_OPC demonstrated an ASR expansion rate approximately three times higher than that of NGA_OPC. This was attributed to the dense structure of HGA_OPC, which resulted in greater expansion than that of NGA_OPC. However, with the incorporation of SCMs into both HGA and NGA, a significant reduction in ASR expansion was observed. This was attributed to the delayed ASR of GA due to alkali activation or the pozzolanic reaction of the SCMs. Continuous exposure to the AMBT environment can lead to the destruction of GA. This was caused by the inner ASR that originated from the surface crack of the GA, which resulted in a reduction in the flexural strength of the mortar. The HGA with SF exhibited the highest resistance to ASR expansion and residual mechanical properties’ degradation. Therefore, various durability and long-term performance-monitoring studies on ultra-high-performance concrete or high-strength cementitious composites with very high SF contents and GA can be conducted.