Titanium white waste acid (TWWA) was used to dissolve the representative elements from red mud (RM) to achieve the goal of “treating waste with waste.” The leaching parameters on the leaching efficiency of Na, Sc, and Al were investigated, in which the analysis of XRD and SEM–EDS on RM and leaching residue was performed. The leaching kinetics of Na, Sc, and Al was studied with unreacted shrinking core model (USCM). The results show that the dealkalization efficiency was close to 100%, and the leaching efficiency of Sc and Al was 82% and 75%, respectively. Cancrinite was dissolved from RM, and then the elements such as Na, Al, and Ca reacted with H2SO4 of TWWA. Na existed in the leaching liquor in the form of ions. Ca reacted with sulfuric acid to form anhydrite, which existed in the leaching residue. The particles of RM became smaller and dispersed with each other by acid leaching. The leaching apparent activation energy of Na, Sc, and Al was 4.947 kJ/mol, 6.361 kJ/mol, and 31.666 kJ/mol, respectively. The leaching kinetic equation of Na, Sc, and Al was 1???(1???a)2/3?=?0.084·exp[??595.05/T]·t by external diffusion, 1???2a/3???(1???a)2/3?=?0.021·exp[??765.16/T]·t by internal diffusion, and ln(1???a)/3?+?(1???a)?2/3 – 1?=?67.12·exp[??3808.8/T]·t by joint action, respectively.