Nanozymes are nanomaterials with catalytic properties similar to those of natural enzymes, and they have recently been collectively identified as a class of innovative artificial enzymes. Nanozymes are widely used in various fields, such as biomedicine, due to their high catalytic activity and stability. Nanozymes can trigger changes in reactive oxygen species (ROS) levels in cells and the activation of inflammasomes, leading to the programmed cell death (PCD), including the pyroptosis, ferroptosis, and autophagy, of tumor cells. In addition, some nanozymes consume glucose, starving cancer cells and thus accelerating tumor cell death. In addition, the electric charge of the structure and the catalytic activity of nanozymes are sensitive to external factors such as light and electric and magnetic fields. Therefore, nanozymes can be used with different therapeutic methods, such as chemodynamic therapy (CDT), photodynamic therapy (PDT) and sonodynamic therapy (SDT), to achieve highly efficient antitumor effects. Many cancer therapies induce tumor cell death via the pyroptosis, ferroptosis, and autophagy of tumor cells mediated by nanozymes. We review the mechanisms of pyroptosis, ferroptosis, and autophagy in tumor development, as well as the potential application of nanozymes to regulate pyroptosis, ferroptosis, and autophagy in tumor cells.