Recycled scrap and waste are used in the production of copper and copper alloys. Cable scrap containing impurities of non-ferrous and ferrous metals is often used as copper scrap. Herein, we propose a novel steam-air oxidation method for the purification of copper alloys. In this method, the melt surface was blown with a steam-air mixture supplied to the melting furnace using a specially manufactured device. Technological parameters ensuring the effective removal of iron, tin, lead, and zinc impurities from the copper melt were determined experimentally. The melt oxidation degree, oxidizer consumption, and duration of the transition of impurities into slag and the gas phase were found to be the key parameters affecting the remelting refining of copper scrap. The technological parameters for the oxidation refining of the melt were optimized using the evolutionary solution search method in order to improve the efficiency of the process and reduce the deoxidizer consumption. It was found that to achieve the maximum efficiency of copper refining, it is necessary to ensure the optimal steam-air oxidation of the melt with oxygen dissolved in it. The results demonstrated the applicability of steam-air oxidation in the refining of copper scrap containing more than 1.6% impurities (including iron, tin, lead, and zinc) to obtain copper melts with chemical compositions corresponding to grades M0 and M1.