The Kingdom of Saudi Arabia (KSA) has millions of date palm trees for commercial scale date-fruit production. The respective industry also generates agricultural waste including date palm tree branches. This rich bio-resource can be used for several beneficial applications. The present study therefore investigated the application of granular activated carbon (GAC) produced using date palm tree branches to successfully remove phenol, p-cresol, and copper from synthetic wastewater. The respective adsorption equilibrium results fitted well to the Langmuir-type adsorption isotherm. Furthermore, the pH-dependent adsorption results both for phenol and p-cresol appeared to follow an anionic-type adsorption behavior (i.e., decreasing adsorption with an increase in aqueous phase equilibrium pH). However, the pH-dependent adsorption finding for copper showed a cationic-type adsorption behavior. These adsorption trends were explained employing the pH-dependent speciation of the respective pollutants. In general, findings from the present work indicate that a high-specific-surface-area (SSABET) GAC material from the date palm tree branches can be successfully employed for aqueous phase pollution control.