An environmentally sound process for the extraction of neodymium (Nd) from magnet scrap was devised and its feasibility was demonstrated. The developed Nd extraction apparatus circulates the magnesium (Mg) as an extraction medium by maintaining a temperature difference within the reaction vessel, thus achieving continuous extraction of metal Nd from scrap, re-extraction of Mg from a Mg–Nd alloy, and finally, pure Nd metal with 97.7% purity was directly recovered from magnet scrap without oxidation. The concept of “scrap combination” for recycling variable materials, that is demonstrated in this study, is an important technology that can be instrumental in creating a highly developed self-sustainable society.