For recovering Ni, Co, and Mn from lithium-ion batteries, traditional chemical precipitation methods demonstrate low selectivity and significantly contribute to environmental pollution. This study proposes a separation recovery technique for transition metals, specifically Ni, Co, and Mn, from spent LIBs, involving "acid dissolution" and "multistage oxidation precipitation". More than 98 % of transition metals can be extracted from spent LIBs using a low acid concentration (0.5 M) without reducing agents. The feasibility of separating different metals via multistage oxidation precipitation, based on their different electrode potentials for oxidizing Me2+ (Me=Mn/Co/Ni), was confirmed. The combination of oxidizing agent S2O8 2- and the precipitant OH- was universally applied to the fractional precipitation of Mn, Co, and Ni respectively. About 99 % of Mn, 97.06 % Co, and 96.62 % Ni could be precipitated sequentially by changing the concentrations of S2O8 2- and the pH value of solution. XRD, XPS, XRF, ICP-MS and other methods were employed to elucidate the mechanism behind the multistage oxidation precipitation of target metal compounds, exploiting the differential electrode potentials for oxidizing Me2+ ions. This technique surpasses traditional solvent extraction in cost-effectiveness and selectivity, showing promise for large-scale industrial applications in recovering Mn, Co, and Ni.