The individual effect of sodium hydroxide (NaOH) and magnesium chloride (MgCl2) on the performance of magnesia-based cement is the main focus of this study. Different magnesium oxide–glass waste (MgO–GW) mixtures of MgO-to-SiO2 molar ratios (MgO/SiO2) of 1, 2, and 3 were prepared and characterized. The results revealed that the mixture having MgO/SiO2=2 showed the best performance at all curing ages. The addition of 3% by weight NaOH significantly enhanced the mechanical properties of the MgO–GW mixture at MgO/SiO2=2. Further addition of NaOH (5% and 7% by weight) caused a notable reduction in the compressive strength values, suggesting the negative effect of high NaOH content on the binding capacity of the produced binder. Increasing the MgCl2 content up to 5% by weight improved the performance of the fabricated cement; meanwhile, the addition of 7% by weight MgCl2 showed the lowest effect. Furthermore, pH is regarded as the key point that affects the performance of magnesia-based cement materials. Two hydration mechanisms were identified, depending on the type of chemical admixture. NaOH increased the pH of the cementitious system, accompanied by speeding up the formation rate of magnesium silicate hydrate (M-S-H) through the improvement of the dissolution of the silicate network within the GW material. Another mechanism was detected in the MgCl2–MgO–GW composite, in which an extra magnesium oxychloride phase (Phase 5: 5 Mg (OH)2·MgCl2·8H2O) was formed besides M–S–H, yielding hardened samples with the highest mechanical properties. Hence, the results herein show that desirable NaOH and MgCl2 contents enhance the feasibility of utilizing GW to produce a high-performance, eco-friendly binder.