Developing nanomaterial-based enzyme mimics for DNA cleavage is an interesting challenge and it has many potential applications. Single-layered graphene oxide (GO) is an excellent platform for DNA adsorption. In addition, GO has been employed for photosensitized generation of reactive oxygen species (ROS). Herein, we demonstrate that GO sheets could cleave DNA as a nuclease mimicking nanozyme in the presence of UV or blue light. For various DNA sequences and lengths, well-defined product bands were observed along with photobleaching of the fluorophore label on the DNA. Different from previously reported GO cleavage of DNA, our method did not require metal ions such as Cu2+. Fluorescence spectroscopy suggested a high adsorption affinity between GO and DNA. For comparison, although zero-dimensional fluorescent carbon dots (C-dots) had higher photosensitivity in terms of producing ROS, their cleavage activity was much lower and only smeared cleavage products were observed, indicating that the ROS acted on the DNA in solution. Based on the results, GO behaved like a classic heterogeneous catalyst following substrate adsorption, reaction, and product desorption steps. This simple strategy may help in the design of new nanozymes by introducing light.