Mineral carbonation of alkaline wastes is a promising route for carbon dioxide (CO₂) capture and utilization. An exploration of the carbonation potential of relatively inert alkaline wastes is important to develop mineral carbonation. Large amounts of coal fly ash are generated from coal-fired power plants and must be treated. A fundamental study of the circular indirect carbonation of coal fly ash was proposed and fly-ash leaching, calcium carbonate (CaCO₃) precipitation, and solution regeneration with bipolar membrane electrodialysis (BPED) stages were investigated. In the leaching stage, the nitric acid/calcium ratio affected the solution pH and impurity concentration. The leaching behavior of impurities was related mainly to colloidal precipitation. Approximately 97.3% calcium in solution reacted to form precipitated CaCO₃, and a higher-purity CaCO₃ precipitate was obtained when a lower nitric acid/calcium ratio was used in the leaching stage. The CO₂ conversion was 92.9% and the CO₂ uptake efficiency was ~0.011 g-CO₂/g-fly ash, which can be improved by optimizing the liquor purification process. Fundamental liquor purification was performed. Solution regeneration by BPED was evaluated by investigating the effect of electric potential and current density on the regeneration yield, current efficiency, and power consumption. A comprehensive assessment, including cost and CO₂ balance, was conducted, and future interesting research on circular indirect carbonation was suggested.