Recycling of valuable metals from secondary resources such as waste Li-ion batteries (LIBs) has recently attracted significant attention due to the depletion of high-grade natural resources and increasing interest in the circular economy of metals. In this article, the sulfuric acid leaching of industrially produced waste LIBs scraps with 23.6% cobalt (Co), 3.6% lithium (Li) and 6.2% copper (Cu) was investigated. The industrially produced LIBs scraps were shown to provide higher Li and Co leaching extractions compared to dissolution of corresponding amount of pure LiCoO2. In addition, with the addition of ascorbic acid as reducing agent, copper extraction showed decrease, opposite to Co and Li. Based on this, we propose a new method for the selective leaching of battery metals Co and Li from the industrially crushed LIBs waste at high solid/liquid ratio (S/L) that leaves impurities like Cu in the solid residue. Using ascorbic acid (C6H8O6) as reductant, the optimum conditions for LIBs leaching were found to be T = 80 °C, t = 90 min, [H2SO4] = 2 M, [C6H8O6] = 0.11 M and S/L = 200 g/L. This resulted in leaching efficiencies of 95.7% for Li and 93.8% for Co, whereas in contrast, Cu extraction was only 0.7%. Consequently, the proposed leaching method produces a pregnant leach solution (PLS) with high Li (7.0 g/L) and Co (44.4 g/L) concentration as well as a leach residue rich in Cu (up to 12 wt%) that is suitable as a feed fraction for primary or secondary copper production.