Copper-containing compounds known as Casiopeı́nas are biologically active molecules which show promising antineoplastic effects against several cancer types. Two possible hypotheses regarding the mode of action of the Casiopeı́nas have emerged from the experimental evidence: the generation of reactive oxygen species or the ability of the compounds to bind and interact with nucleic acids. Using robust molecular dynamics simulations, we investigate the interaction of four different Casiopeı́nas with the DNA duplex d(GCACGAACGAACGAACGC). The studied copper complexes contain either 4-7- or 5-6-substituted dimethyl phenanthroline as the primary ligand and either glycinate or acetylacetonate as the secondary ligand. For statistical significance and to reduce bias in the simulations, four molecules of each copper compound were manually placed at a distance of 10 Å away from the DNA and 20 independent molecular dynamics simulations were performed, each reaching at least 30 μs. This time scale allows us to reproduce expected DNA terminal base-pair fraying and also to observe intercalation/base-pair eversion events generated by the compounds interacting with DNA. The results reveal that the secondary ligand is the guide toward the mode of binding between the copper complex and DNA in which glycinate prefers minor-groove binding and acetylacetonate produces base-pair eversion and intercalation. The CuII complexes containing glycinate interact within the DNA minor groove which are stabilized principally by the hydrogen bonds formed between the amino group of the aminoacidate moiety, whereas the compounds with the acetylacetonate do not present a stable network of hydrogen bonds and the ligand interactions enhance DNA breathing dynamics that result in base-pair eversion.