In the present study, a dinuclear bis(μ-acetate) dicopper(II) complex [Cu2L2(μ1.1-CH3COO-)2] has been synthesized from a tridentate NNO Schiff Base ligand L (L = 2,4-dibromo-6-((3-(methylamino)propylimino)methyl)phenol) and characterized by elemental, ultraviolet-visible (UV-vis), Fourier transform infrared (FTIR), 1H NMR, and electrospray ionization-mass spectrometry (ESI-MS) spectroscopic studies. The single-crystal X-ray structure, different noncovalent interactions, Hirshfeld surface analysis, and density functional theory (DFT) studies of the dinuclear complex were determined by crystallographic computational studies. The structural study exposed that the complex consists of the penta-coordinated double μ1.1-acetato-bridged dinuclear units of Cu(II), and it is a centrosymmetric dimer in which the center of inversion lies at the midpoint of two Cu(II) ions. Hirshfeld surface and DFT studies pointed out the probable potentiality of the crystal in prospective binding with the protein. This was experimentally verified by carrying out the binding interaction studies against bovine serum albumin (BSA) protein using various spectroscopic methods. It was observed that the copper(II) complex could strongly bind to BSA and could quench the intrinsic fluorescence of BSA. Further, the studied complex was appraised for cell viability studies against SiHa cancer cells. It is observed that cell viability increases with time, demonstrating the biocompatible nature of the complex.