The green transition initiatives and exploitation of renewable energy sources require the sustainable development of rare earth (RE)-based permanent magnets prominent technologies like wind turbine generators and electric vehicles. The recycling of RE-based permanent magnets is necessary for the future supply of critical rare-earth elements. The short-loop recycling strategies to directly reprocess Nd-Fe-B magnet waste are economically attractive and practical alternatives to conventional hydro- and pyrometallurgical processes. This study focuses on the development of a procedure to extract the (Nd, Pr) ₂Fe ₁₄B hard-magnetic phase from sintered Nd-Fe-B magnets. The extraction is achieved through preferential chemical leaching of the secondary, RE-rich phases using 1 M citric acid. Before the acid treatment, the magnets were pulverized through hydrogen decrepitation (HD) to increase the material’s surface-to-volume ratio. The as-pulverized Nd-Fe-B powder was subsequently exposed to a 1 M citric acid solution. The effect of leaching time (5–120 min) on the phase composition and magnetic properties was studied. The results of the microstructural (SEM) and compositional (ICP-MS) analyses and the study of thermal degassing profiles revealed that the RE-rich phase is preferentially leached within 5–15 min of reaction time. Leaching of the secondary phases from the magnet’s multi-phase microstructure is governed by the negative electrochemical potential of Nd and Pr. The extraction of (Nd, Pr) ₂Fe ₁₄B grains by the proposed acid leaching approach is compatible with the existing hydrogen processing of magnetic scrap (HPMS) technologies. The use of mild organic acid as a leaching medium makes the leaching process environmentally friendly, as the leaching medium can be easily neutralized after the reaction is completed.