Background/Objectives: Cu(II) complexes with polypyridine ligands have shown carcinogenic activity already described in the literature and appear as a possible alternative to cisplatin, which has several side effects. In view of this, four Cu(II) complexes with the formulas [Cu(L1)(H₂O)₂](PF₆)₂ (A1) and [Cu(L2)(H₂O)₂](PF₆)₂ (A2), [Cu(L1)(bipy)](PF₆)₂ (B1) and [Cu(L2)(bipy)](PF₆)₂ (B2) were synthesized, where L1 = dipyrido[1,2,5]oxadiazolo[3,4-b]quinoxaline, L2 = 6,7-dicyanodipyrido[2,2-d:2,3-f]quinoxaline, and bipy = 2,2′-bipyridine. Methods: The proposed structures supported characterization techniques (molar conductivity, elemental analyses, absorption spectroscopy in the infrared region, and UV–vis). The interaction of the complexes with DNA was evaluated through an ethidium bromide displacement assay, complemented by theoretical studies using molecular docking. Additionally, the cytotoxic activity of the complexes was tested against DU 145 (prostate tumor), MCF-7 (breast tumor), and PNT-2 (non-tumor prostate) cell lines, with all complexes showing promising results. Results: Among them, complex B1 exhibited the highest number of DNA contacts in molecular docking studies, a binding constant of 3.7 × 10⁶ in the ethidium bromide displacement assay. It was the most selective complex (IS = 5.43) for the DU 145 (prostate tumor) cell line, demonstrating greater selectivity than cisplatin. Conclusions: This study has demonstrated the potential of the Cu(II) complexes obtained, which could be an alternative to platinum complexes in the future