Supplying critical metals such as cobalt, lithium, and nickel, to achieve sustainable development goals will be one of the most important concerns in the coming decades. A significant challenge in this area is the separation of some similar elements, such as nickel and cobalt. This study proposes a novel and eco-friendly process to selectively recover cobalt from nickel and manganese. The process includes two leaching stages in a microwave environment: (1) leaching by glycine to separate Ni and Mn and (2) leaching by oxalic acid to separate cobalt from other elements and precipitate it as cobalt oxalate dihydrate. In the first leaching stage, response surface methodology (RSM) was employed to optimize leaching parameters. Under the optimal conditions (3 M of glycine, 0.01 M ascorbic acid, 15 min, pH 9, 500-W microwave power, and a solid-to-liquid (S/L) ratio of 5:100), the average leaching efficiencies were 96.32% for nickel, 91.97% for manganese, and 12.11% for cobalt. In the second leaching stage, 98% of cobalt was successfully precipitated as cobalt oxalate dihydrate by oxalic acid in the microwave environment, with over 87% of the total cobalt ideally recovered from other elements.