Mixed ligand copper(II) complexes [Cu(L1)(bpy)](ClO₄)₂1 and [Cu(L2)(bpy)](ClO₄)₂2 (where L1 = 1-(anthracen-9-yl)-N,N-bis(pyridin-2-ylmethyl)methanamine, L2 = 1-(pyren-1-yl)-N,N-bis(pyridin-2-ylmethyl)methanamine and bpy = 2,2′-bipyridine) were synthesised and characterised thoroughly via different analytical and spectroscopic techniques i.e., UV-vis spectroscopy, fluorescence spectroscopy, FT-IR spectroscopy, HRMS and EPR spectroscopy. The molecular structures of the synthesised complexes were obtained using the single-crystal X-ray diffraction technique. Both complexes exhibited penta-coordinated and acquired distorted square pyramidal geometry. The redox behaviour of complexes 1 and 2 was investigated by employing cyclic voltammetry. The DNA binding study was carried out by UV-vis spectrophotometry using double-stranded salmon sperm DNA (ds-ss-DNA). The binding constant (K_b) values of 1 and 2 were 0.11 × 10⁴ M⁻¹ and 1.05 × 10⁴ M⁻¹, respectively, which indicates that 2 has better binding ability than 1. This might be due to the higher conjugative abilities with the extended surface area of the aromatic pyrene ring compared to the anthracene moiety. The fluorescence quenching experiments were also performed with EB bound DNA (EB–DNA) and Stern–Volmer constant (K_SV) values were calculated as 1.23 × 10⁵ M⁻¹ and 1.39 × 10⁵ M⁻¹ for 1 and 2, respectively, suggesting that 2 showed stronger interaction with ss-DNA than 1. The molecular docking data support the DNA-binding studies, with the sites and mode of interactions against B-DNA varying with 1 and 2. Evaluation of the DNA binding properties of the complexes to linearized plasmid DNA indicated that 2 had modest DNA binding properties, which is a pre-requisite for a genotoxic agent. The effect of 1 and 2 on cell survival was analysed using HeLa cells by MTT assay and it was observed that the IC₅₀ values of 1 and 2 were 43.7 μM and 18.6 μM, respectively. Our study paves the way for the designing of bio-inspired novel mixed metal complexes, which shows promising results for further exploration of molecular and mechanistic studies towards the development of non-platinum based economical metallodrugs.