After mechanical pre-treatment, the typical hydrometallurgical route of NdFeB magnet recycling starts with leaching in acidic solutions. However, due to the high concentration of iron ions in the leaching solution, the selective recovery of rare earths from the solution is challenging. In our work, the selective precipitation of rare earth oxalates as a potential separation method was proposed. The precipitation of neodymium oxalate was first tested on model solutions, which was then followed by experimental tests carried out on real solutions after the leaching of NdFeB magnets. The recovery of rare earths in the form of oxalates was investigated with the use of different amounts of oxalic acid in relation to its stoichiometric amount. The most efficient separation of rare earths was observed in the case where sulfuric acid was used for leaching. The use of oxalic acid in stoichiometric amounts resulted in the precipitation of about 93% of all rare earths present in the solution, whereas the concentration of Fe and other elements (Ni, Co, and B) practically did not change. An increase in oxalic acid of 20% and 40% more than the stoichiometric amount (100%) led to the increase in the precipitation efficiency of rare earths to 96.7% and 98.1%, respectively. However, the use of oxalic acid in a 1.4 ratio caused a 7% decrease in Fe concentration, which suggests Fe co-precipitation. In order to investigate a possibility of further increasing the separation of rare earths from iron, an additional method was tested, in which iron was first oxidized from Fe2+ to Fe3+ before the precipitation of rare earth oxalates.