Oxidative stress, caused by an imbalance in the formation and elimination of reactive oxygen and nitrogen species, plays an important role in brain aging and the development of neurodegenerative diseases. In this study, I investigated the toxic effect of copper on SH-SY5Y neuroblastoma cells. By MTT test, trypan blue exclusion assay, and ATP level measurement, I found a significant decline in SH-SY5Y cell survival after copper treatment. Copper has increased the production of reactive species, which at high values cause oxidative damage, and reduced glutathione levels. It also caused chromatin condensation without caspase 3 and 7 activation, as well as cell membrane damage, from which I conclude that copper caused programmed cell death via caspase-independent activation and necrosis. At the protein level, there was increased expression of p53 and PARP-1 proteins, while NME1 protein expression decreased. Administration of the PARP-1 protein inhibitor (PJ34) did not affect toxicity, whereas administration of the p53 protein inhibitor (pifitrin-α) caused an increase in copper toxicity. The flavonoid myricetin enhanced the cytotoxicity of copper by its prooxidative action. The obtained results clarify the mechanism of prooxidative action of copper at the cellular and molecular level, which could contribute to the development of new pharmacological approaches in the prevention and treatment of neurodegenerative diseases.