The environmental and economic benefits of recycling spent Nd-Fe-B magnets are becoming increasingly important. Nevertheless, the reprocessing of this type of material by conventional processes remains a challenge due to the difficulties of rare earth elements (REEs) and Fe separation, low products purity and large-scale generation of boron wastewater. This research presents an effective approach for the comprehensive recovery of REEs, iron and boron from Nd-Fe-B magnet wastes. Investigations of the initial roasting pretreatment showed it to be an effective method that aids the subsequent selective separation of REEs, with the most suitable temperature determined to be 800 °C. During the following selective hydrochloric acid pressure leaching of the roasted magnet, the addition of 2 g/L NaNO3 was found to significantly improve the separation of REEs and B from Fe. The results indicated that almost 99% of REEs and 97% of B could be extracted, whilst in contrast, less than 0.1% of iron dissolved, to leave a hematite rich residue. The extracted REEs were then directly precipitated as oxalates with >99% extraction and 99.95% purity at a value n(oxalic acid)/n(REEs) of 1, resulting in significant improvements to oxalic acid consumption and REEs product purity. In the final step, 99.5% of boron was recovered via a three-stage counter current extraction with 30% (v/v) (EHD) and 70% (v/v) sulfonated kerosene. These findings demonstrate that high recoveries of REEs, Fe and B are achievable with hydrochloric acid pressure leaching followed oxalate precipitation and boron recovery.