Numerous studies have been conducted on the removal of heavy and toxic metals using protonated dry alginate beads (PDABs) as a cation exchanger. However, there is a scarcity of research on the kinetics of copper elution with biosorbents, despite the necessity of restoring them to their original state with undiminished biosorption capacity for reuse. This study analyzes the parameters that directly affect the elution rate of copper ions from PDABs. The parameters examined include temperature (5–80 °C), sulfuric acid concentration (0.0005–0.0153 M), stirring speed (0–500 rev min−1), and different acids (HNO3, HCl, and HClO4). Additionally, the stability of alginate was assessed over multiple cycles. The results indicate that the elution mechanism is governed by ion exchange between copper ions and protons. The copper elution rate was significantly influenced by temperature and H2SO4 concentration, achieving an elution efficiency of 98.6% at 80 °C and an H2SO4 concentration of 0.0056 M. The kinetics of copper ion elution were adequately described by the Lagergren pseudo-first-order model. The dependence of copper elution on sulfuric acid concentration was found to be of the order of 0.4. Furthermore, intrinsic rate constants were determined, and an activation energy of 9.2 kJ mol−1 was obtained within the studied temperature range. These findings indicate that copper elution is a chemically controlled process.