To synergistically recover alumina and alkali from red mud (RM), the structural stability and conversion mechanism of hydroandradite (HA) from hydrogarnet (HG) were investigated via the First-principles, XRF, XRD, PSD and SEM methods, and a novel hydrothermal process based on the conversion principle was finally proposed. The crystal structure simulation shows that the HA with varied silicon saturation coefficients is more stable than HG, and the HA with a high iron substitution coefficient is more difficult to be converted from HG. The (110) plane of Fe₂O₃ is easier to combine with HG to form HA, and the binding energy is 81.93 kJ/mol. The effects of raw material ratio, solution concentration and hydrothermal parameters on the conversion from HG to HA were revealed, and the optimal conditions for the alumina recovery were obtained. The recovery efficiencies of alumina and Na₂O from the RM are 63.06% and 97.34%, respectively, and the Na₂O content in the treated RM is only 0.13%.