Two new copper (II) carboxylates viz. [Cu2(μ–2-chlorobenzoato-O,O')4(2-methoxybenzaldehyde)2] (1) and [Cu(μ–3,5-dinitrobenzoato-CO,O)(μ–3,5-dinitrobenzoato-NO,O)][Cu2(μ–3,5-dinitrobenzoato-CO,O′)](μ1MeOH)2 (2) containing 2-chlorobenzoic acid and 3,5-dinitrobenzoic acid respectively were synthesized, and characterized by elemental analyses, spectroscopic methods, topological analysis and single crystal XRD studies. Moreover, the synthesized complexes have been screened for the DNA binding ability through UV-Visible and fluorescence spectroscopy indicating moderately strong non-intercalative mode of interaction. Structural studies reveals that compound 1 possesses dinuclear paddle-wheel structure whereas compound 2 is 3D polymer. Asymmetric/monoclinic unit of compound 2 contains a mononuclear unit in combination with a dinuclear entity. DFT calculations combined with QTAIM and NCI plot computational tools have been used to analyze their solid-state supramolecular assemblies focusing on the role of halogen···halogen interactions in 1 and π-hole O···N pnictogen bonding in 2 involving the nitro groups. Finally, the dye adsorption property of the complexes was studied to ascertain their efficacy in removal of toxic dye molecules from aqueous medium. Compound 2 exhibits moderate dye removal efficiency.