This study investigates the efficacy of adsorbents from locally sourced olive waste—encompassing olive skins, leaves, and pits, recovered from the initial centrifugation of olives (OWP)—and a composite with sodium alginate (OWPSA) for the removal of Cu2+ ions from synthetic wastewater. Experimental analyses conducted at room temperature, with an initial Cu2+ concentration of 50 mg/L and a solid/liquid ratio of 1 g/L, showed that the removal efficiencies were approximately 79.54% and 94.54% for OWP and OWPSA, respectively, highlighting the positive impact of alginate on adsorption capacity. Utilizing statistical physics isotherm models, particularly the single-layer model coupled to real gas (SLMRG), allowed us to robustly fit the experimental data, providing insights into the adsorption mechanisms. Thermodynamic parameters affirmed the spontaneity and endothermic nature of the processes. Adsorption kinetics were interpreted effectively using the pseudo-second-order (PSO) model. Molecular modeling investigations, including the conductor-like screening model for real solvents (COSMO-RS), density functional theory (DFT), and atom-in-molecule (AIM) analysis, unveiled intricate molecular interactions among the adsorbent components—cellulose, hemicellulose, lignin, and alginate—and the pollutant Cu2+, confirming their physically interactive nature. These findings emphasize the synergistic application of experimental and theoretical approaches, providing a comprehensive understanding of copper adsorption dynamics at the molecular level. This methodology holds promise for unraveling intricate processes across various adsorbent materials in wastewater treatment applications.