The growing demand for Li-ion batteries (LIBs) has made their postconsumer recycling an imperative need toward the recovery of valuable metals, such as cobalt and nickel. Nevertheless, their recovery and separation from active cathode materials in LIBs, via an efficient and environmentally friendly process, have remained a challenge. In this work, we approach a simple and green method for the selective separation of nickel ions from mixed cobalt–nickel aqueous solutions under mild conditions. We discovered that the bioinspired microporous metal−organic framework (MOF) SU-101 is a selective sorbent toward Ni2+ ions at pH 5–7 but does not adsorb Co2+ ions. According to the Freundlich isotherm, the adsorption capacity toward Ni2+ reached 100.9 mg·g–1, while a near-zero adsorption capacity was found for Co2+ ions. Ni2+ removal from aqueous solutions was performed under mild conditions (22 °C and pH 5), with a high yield up to 96%. The presence of Ni2+ ions adsorbed on the surface of the material has been proven by solid-state 1H nuclear magnetic resonance spectroscopy. Finally, the separation of Ni2+ from Co2+ from binary solutions was obtained with approximately 30% yield for Ni2+, with a near-zero adsorption of Co2+, which has been demonstrated by UV–vis spectroscopy. The ion adsorption process of Ni2+ and Co2+ ions was additionally studied by means of classical molecular dynamics calculations (force fields), which showed that the Ni2+ ions were more prone to enter the MOF canals by replacing some of their coordinated water molecules. These results offer a green pathway toward the recycling and separation of valuable metals from cobalt-containing LIBs while providing a sustainable route for waste valorization in a circular economy.