The recycling of lithium-ion batteries is increasingly important for both resource recovery and environmental protection. However, the complex composition of cathode and anode materials in these batteries makes the efficient separation of metal mixtures challenging. Hydrometallurgical methods, particularly liquid extraction, provide an effective means of separating metal ions, though they require periodic updates to their extraction systems. This study introduces a hydrophobic deep eutectic solvent composed of trioctylphosphine oxide, di(2-ethylhexyl)phosphoric acid, and menthol, which is effective for separating Ti(IV), Co(II), Mn(II), Ni(II), and Li+ ions from hydrochloric acid leachates of NMC (LiNixMnyCo1−x−yO2) batteries with LTO (Li4Ti5O12) anodes. By optimising the molar composition of the trioctylphosphine oxide/di(2-ethylhexyl)phosphoric acid/menthol mixture to a 4:1:5 ratio, high extraction efficiency was achieved. The solvent demonstrated stability over 10 cycles, and conditions for its regeneration were successfully established. At room temperature, the DES exhibited a density of 0.89 g/mL and a viscosity of 56 mPa·s, which are suitable for laboratory-scale extraction processes. Experimental results from a laboratory setup with mixer-settlers confirmed the efficiency of separating Ti(IV) and Co(II) ions in the context of their extraction kinetics.