The activity and interacting ability of a polyamidoamine (PAMAM) dendrimer modified with 4-N-methylpiperazine-1,8-naphthalimide units (termed D) and complexed by Cu(ii) ions, towards healthy and cancer cells were studied. Comparative electron paramagnetic resonance (EPR) studies of the Cu(ii)-D complex are presented: coordination mode, chemical structure, flexibility and stability of these complexes, in the absence and presence of myeloid cancer cells and peripheral blood mononuclear cells (PBMC). The interactions of Cu(ii) ions in the biological media at different equilibrium times were studied, highlighting different stability and interacting conditions with the cells. Furthermore, flow cytometry and confocal analysis, trace the peculiar properties of the dendrimers in PBMC and U937 cells. Indeed, a new probe (Fly) was used as a potential fluorescent tool for biological imaging of Cu(ii). The study highlights that dendrimer and, mainly, the Cu(ii) metallodendrimer are cytotoxic agents for the cells, specifically for U937 tumor cells, inducing mitochondrial dysfunction, ROS increase and lysosome involvement. The metallodendrimer shows antitumor selectivity, fewer affecting healthy PBMC, inducing a massive apoptotic cell death on U937 cells, in line with the high stability of this complex, as verified by EPR studies. The results underline the potentiality of this metallodendrimer to be used as anticancer drug.