Ways to reduce cement-related carbon emissions are actively sought. One possible solution is partial substitution of Portland cement by alkali-reactive glass. We report on low-CO2 glass compositions that have high alkali solubility derived from industrial basaltic stone wool compositions. We found that highly alkali-soluble glasses can be formed with glass compositions that in principle can be made using silicate minerals which have no raw material-related CO2 emissions. The reason behind the reactivity of these glasses is thought to be caused by the dilution of the main network-forming species, silicon, which is further enhanced by phase separation, forming phases with high-silicon and low-silicon concentrations. Phase separation in alumina-rich samples is further studied and occurs at moderate cooling rates. The effect of glass-glass phase separation is discussed in the context of reactive glasses in cementitious systems. The results indicate that controlled phase separation could decouple CO2 emissions from the reactivity of glassy supplementary cementitious materials.