A series of derivatives of the Zr-based MOF UiO-66 were synthesized, fully characterized, and tested for their efficiency in the adsorption and removal of the highly toxic elements lead (Pb(II)), cadmium (Cd(II)), arsenate As(V), and selenite Se(IV). Different structural engineering techniques were employed to alter the properties of the Zr-MOFs, such as linker functionalization and defect creation to increase the density of adsorption sites. The functionalization of the UiO-66-based structures with carboxylate groups increased the removal efficiency of Pb(II) cations by more than 70% and that of Cd(II) cations by more than 60% to reach 125.2 and 69.1 mg/g, respectively. Moreover, the induced cluster defects were found to be the preferred adsorption sites of the anion pollutants. The adsorption of As(V) and Se(IV) by the high-defect UiO-66-200FA was 132.5 and 30.8 mg/g, respectively, which was higher than that of the less defect UiO-66, while almost no adsorption was achieved by UiO-66(COOH)2. Furthermore, a multivariate (MTV-MOF) approach was employed to investigate the effect of the functional groups on the diffusion of the adsorbates within the porous networks. Interestingly, adsorption equilibrium was reached within minutes for the best-performing MOFs, highlighting their potential to be used in practical water treatment applications. Finally, chemical adsorption seemed to be dominant among binding mechanisms for all the pollutants, which were analyzed in detail to determine the characteristics that govern the adsorption efficiency of UiO-66-based adsorbents. The conclusions provided by this comprehensive study help serve as a guideline for future researchers aiming to employ UiO-66-based adsorbents by providing them with a deep understanding of the design strategies required to maximize the performance of this robust MOF.