There are many factors that determine the toxicity of nanoparticles, so that each nanoparticle is to be considered separately for its toxicity, that is for its undesired effects on the cell activity. In the case of CuO and ZnO, both are cited [1] as causing damage to the cell membrane. ZnO is cited [1] as affecting cell morphology, causing DNA damage, etc.
[1] H Bahadar et al., Toxicity of Nanoparticles and an Overview of Current
Experimental Models: Article Toxicity of Nanoparticles and an Overview of Current Experim...