Improvement in mechanical properties of non-cement mortar using ASTM Class C fly ash (FA) containing high amounts of CaO produced from a fluidized bed-type boiler and blast furnace slag (BS) was studied. This type of FA is used to carbonate non-cement mortar under supercritical conditions for $CO_2$ fixation, and it cannot be recycled and reclaimed easily because of the presence of high amounts CaO. Specimens of non-cement mortar with varied mixing ratios of BS and FA, distilled water, and alkali activators were prepared, aged for 3, 7, and 28 days, and subsequently, supercritically carbonated in a $CO_2$ atmosphere. As a result, an improvement in the mechanical properties of non-cement mortars was expected. $CaCO_3$ was produced in the specimens as a result of carbonation under supercritical conditions. The weight change rate, carbonation rate, phenolphthalein test, and mechanical compressive strength tests were performed on the specimens. In the case of the specimens with only distilled water added, the high pH of the FA increased the reactivity of the BS, thereby enhancing the mechanical properties of the specimen. In the case of the alkali-activated non-cement mortar specimen, the compressive strength increased by 11.2%, to 52 MPa after carbonation under the supercritical condition.