Rare-earth elements (REEs) are increasingly susceptible to supply risks due to their limited geographical availability and growing demand in clean energy applications such as neodymium-iron-boron (NdFeB) magnets used in electric vehicles and wind turbines. When NdFeB magnets are produced, 6–73% of swarf is generated during the manufacturing steps. This paper presents an innovative technology that utilizes copper nitrate to dissolve REEs in NdFeB magnet swarf and subsequently recovers ∼97% of them as mixed rare-earth oxides (REOs) of purity higher than 99.5%. Techno-economic analysis (TEA) and life cycle assessment (LCA) quantified the economic and environmental impacts of adopting the proposed acid-free dissolution technology, projecting a net profit margin of 12–43% and a global warming impact reduction by up to 73% compared to the prevailing REO production routes in China. As copper nitrate is the single largest contributor to the cost and environmental footprint, recycling of copper nitrate was investigated as well as using alternative copper salts (e.g., copper acetate), revealing significant improvements in TEA and LCA results. Dysprosium was a major revenue source, highlighting the importance of targeting electric vehicle magnets that are rich in dysprosium. As the REO market is volatile, sensitivity analysis was employed to evaluate the profitability of the proposed technology under different REO prices over the last 11 years. Overall, our results confirmed the economic and environmental viability of the proposed technology for sustainable recycling of REEs from the NdFeB magnet swarf.