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)2Fe14B 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)2Fe14B 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.