The availability of industrially used supplementary cementitious materials (SCMs, e.g., fly ash) decreases due to the rise in renewable energy sources and recycling technologies. Therefore, it is essential to find alternative SCMs (e.g., waste glass and clay brick powder) that are locally available. Accordingly, in this paper, the mechanochemical activation of clay brick waste (CBW) with abrasive glass powder (GP) and its pozzolanic reactivity are investigated. The mixtures of CBW and GP in mass ratios of 100:0, 75:25, 50:50, and 25:75 were mechanochemically activated for 15, 30, 45, and 60 min. The physical, chemical, and structural changes of the mixtures were examined by X-ray diffractometry, Fourier-transform infrared spectroscopy, scanning electron microscopy, and specific surface area measurements. The pozzolanic reactivity was characterized by the active silica content and the 28-day compressive strength of the binders (a mixture of ordinary Portland cement and activated material). The addition of GP favorably reduced the agglomeration and increased the active silica content of the activated mixtures (e.g., by 7–37% m/m at 15 min of mechanochemical activation). The 60 min of mechanochemical activation and the addition of 50% m/m of GP can increase the compressive strength by approximately 8%. Economically, the addition of 50% m/m of GP was found to be favorable, where only 30 min of mechanochemical activation resulted in a considerable increase in strength compared to that of the ordinary Portland cement.