In this research, the possibility of using sustainable nano-MgO/Ca-alginate beads for efficient sorption of some rare earth metal ions such as neodymium(III) and yttrium(III) from an aqueous acidic solution was explored. The nano-MgO/Ca-alginate beads adsorbent was characterized before and after sorption of Nd(III) and Y(III) using scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FT-IR), energy dispersive X-ray analysis (EDX), and X-ray diffraction (XRD) techniques. Batch sorption parameters were investigated, such as contact time, initial metal ion concentration, and adsorbent dose (V/m). The calculated experimental results showed that the suitable selected sorption conditions were carried out using 100 mg/L of Nd(III) and Y(III) with nano MgO/Ca-alginate beads (contact time = 90 min, pH = 2, V/m = 0.05 L/g). The maximum sorption capacity of 0.1 g of nano MgO/Ca-alginate was found to be 7.85 mg/g and 5.60 mg/g for Nd(III) and Y(III), respectively. The desorption of Nd(III) and Y(III) from the loaded nano MgO/Ca-alginate was achieved with 1.0 M sulfamic acid and found to be 51.0% and 44.2%, respectively. The calculated thermodynamic parameters for the nano MgO/Ca-alginate/Nd/Y system show that the positive charge of ΔHo confirmed the endothermic nature of the sorption process, ΔSo (positive) indicates an increase in reaction system disordering, and ΔGo (negative) indicates a spontaneous process. These kinetic results indicate that the sorption process of Nd(III) and Y(III) on nano MgO/Ca-alginate beads is performed by the chemisorption process.