Two new isostructural coordination compounds of Ni(II) and Mn(II) viz. [Ni(H2O)4(Hdmpz)2]ADS (1) and [Mn(H2O)4(Hdmpz)2]ADS (2) (where, Hdmpz = 3,5-dimethylpyrazole, ADS = anthraquinone-1,5-disulfonate) have been synthesized in aqueous medium at room temperature and characterized them using elemental analysis, TGA, FT-IR, electronic spectroscopy and single crystal X-ray diffraction techniques. Coordination compounds involving ADS anions in the crystal lattice are scarcely reported in the literature. Crystal structure analysis reveals the presence of unconventional O···O dichalcogen bonding interaction between the O-atoms of neighbouring ADS moieties of the compounds. Aromatic π-stacking and unusual charge assisted O‒H···O and C‒H···O hydrogen bonds (CAHBs) are also involved in the stabilization of the crystal structures. Theoretical calculations have been performed to analyze the CAHBs, π-stacking and O···O dichalcogen bonding interactions observed in the solid-state structures of 1 and 2 using DFT calculations, MEP surface analysis, QTAIM and NCI plot index computational tools. The relatively larger interaction energy observed for Ni(II) compound can be attributed to the higher contribution of the CAHBs than that for the Mn(II) complex. The energy associated to the O···O dichalcogen bonding interaction is small (0.6 kcal/mol) and comparable with the weak C‒H···O contact observed in compound 2. In vitro antiproliferative activities of the compounds considering cell cytotoxicity and apoptosis reveal the cytotoxic potential of the compounds in Dalton's Lymphoma (DL) cancer cells with negligible cytotoxicity in normal PBMC cells. Molecular docking simulation of the compounds with antiapoptotic proteins reveals significant affinity of the compounds with the active sites of the antiapoptotic proteins.