In pursuit of carbon neutrality, the demand for metals that are necessary for the development of clean energy technologies is rapidly increasing. Metallurgical waste, such as slag, presents a promising secondary source of these key metals. This research aims to develop an eco-friendly hydrometallurgical process to recover Cu, Ni, and Co from discarded copper/nickel slag. High-pressure acid leaching (HPAL) was used to selectively leach Ni, Cu, and Co from the fayalite slag, yielding high leaching efficiencies of 99.9%, 89.4%, and 99.9%, respectively, with low Fe and Si tenors to the pregnant leach solution (PLS). The solvent extraction (SX) technique utilizing LIX 984N was used to selectively extract and enrich copper from the dilute PLS to about 23 g/L Cu with a very low Fe concentration of 0.05 g/L. Potassium amyl xanthate (PAX) solution was used to form Ni and Co xanthate complexes from the raffinate solution. Nickel was selectively recovered using ammonia solution, while the cobalt xanthate complex was thermally decomposed and recovered as cobalt oxide solids of about 25 wt.% Co. A comprehensive process flowsheet is presented. Furthermore, to realize the real application of the developed slag cleaning process, a preliminary economic evaluation was performed.