Critical raw materials, such as graphite and lithium metal oxides (LMOs), with a high supply risk and high economic importance are present in spent lithium-ion batteries (LIBs). The recovery and recycling of these critical raw materials from LIBs will contribute to the circular economy model, reduce the environmental footprint associated with the mining of these materials, and lower their high supply risk. The main aim of this paper is to present a separation process to recover graphite from black mass (BM) from spent LIB. Simultaneously, LMO and copper (Cu) and aluminum (Al) foils were also recovered as by-products from the process. The process used a combination of simple and/or low environmental footprint technologies, such as sieving, sink-float, citric acid leaching, and milling through ultrasound and soft attrition, to allow separation of the LIB valuable components. Three graphite-rich products (with purities ranging between 74 and 88 wt.% total carbon and a combined yield of 14 wt.%) with three different sizes (<25 µm, <45 µm, and <75 µm), Cu and Al foil fragments, and an LMO-rich precipitate product are delivered. The developed process is simple, using low temperatures and weak acids, and using affordable and scalable equipment available in the market. Its advantage over other LIB recycling processes is that it can be implemented, so to speak, “in your backyard”.