The unique and outstanding physical and chemical properties of aluminosilicate minerals, including zeolites, make them extremely useful in remediation processes. That is due to their demonstrated high efficiency, inexpensiveness, and environmental friendliness in processes aimed on the elimination of heavy metals from water. The paper reports the results of the examination of selectivity of the tested clay minerals and zeolites toward different heavy metals in light of the postulated sorption mechanisms. It was stated that while the most efficient at concurrent removal of lead and copper from aqueous solutions were synthetic zeolites 3A and 10A, smectite was the best in dealing with prolonged pollution with Pb2+ and Cu2+. Determined as one of the parameters in DKR isotherm energy of the process for each combination of sorbate and sorbent, it showed that the dominant mechanism of adsorption on the tested mineral sorbents was physisorption. The exception was kaolinite, for which that energy implied ion exchange as the dominant mechanism of the process.