Single-atom nanozymes (SAzymes) open new possibilities for the development of artificial enzymes that have catalytic activity comparable to that of natural peroxidase (POD). So far, most efforts have focused on the structural modulation of the Fe-N moiety to mimic the metalloprotein heme center. However, non-heme-iron POD with much higher activity, for example, HppE, has not been mimicked successfully due to its structural complexity. Herein, carbon dots (CDs)-supported SAzymes with twisted, nonplanar Fe-ON active sites, highly similar to the non-heme iron center of HppE, was synthesized by exploiting disordered and subnanoscale domains in CDs. The Fe-CDs exhibit an excellent POD activity of 750 units/mg, surpassing the values of conventional SAzymes with planar Fe-N. We further fabricated an activatable Fe-CDs-based therapeutic agent with near-infrared enhanced POD activity, a photothermal effect, and tumor-targeting ability. Our results represent a big step in the design of high-performance SAzymes and provide guidance for future applications for synergistic tumor therapy.