Functional metal-organic frameworks (MOFs), especially those based on sulfur and nitrogen atoms, were frequently applied for the removal of Hg(II) ions. However, a systematic study on the cooperative or competitive roles of -SH and -NH functions in the presence of secondary mechanisms (proton transfer and redox) is still rare. In this work, the UiO-66 framework (Zr(OH)O(BDC), BDC = benzene-1,4-dicarboxylate) was decorated with functional monocarboxylate linkers including glycine (Gly), mercaptopropionic acid (Mer), and cysteine (Cys). Due to the molecular similarity of these functional linkers, the coordination affinity between the amine and thiol sites with Hg(II) ions can be compared, and the effect of proton transfer and redox mechanisms on the possible thiol···Hg(II) and amine···Hg(II) interactions can be investigated. The results show that the Cys@UiO-66 framework can adsorb 1288 mg g of Hg(II), while Mer@UiO-66 and Gly@UiO-66 can adsorb 593 and 313 mg g at pH = 7 and 500 ppm, respectively. This is due to the facts that both the amine and the thiol functions of the Cys@UiO-66 framework show synergism in Hg(II) removal, and the secondary mechanisms reduce the affinity of thiol in Mer@UiO-66 and amine in Gly@UiO-66 frameworks in the removal process of Hg(II) ions. Free -SH sites in Mer@UiO-66 undergo a redox convert to -SOH groups, and free protonated -NH sites in Gly@UiO-66 do not fully deprotonate during Hg(II) removal. Yet, in the case of Cys@UiO-66, free protonated -NH sites are fully deprotonated, and free SH sites did not convert to -SOH groups during Hg(II) removal. These observations show that the redox and proton transfer mechanisms can negatively affect the adsorption capacity of functional MOFs containing free -SH and -NH groups. So, not only the functionalization but also control over secondary mechanisms in the removal process are necessary parameters to improve the affinity between functional MOFs and Hg(II) ions.