As a popular sensing method, colorimetric biosensing has the advantages of convenient operation, low cost, fast response, and easy readout. However, due to the complex structure of nanomaterials, low catalytic activity, and unclear catalytic mechanisms, constructing efficient, stable, and specific artificial biocatalysts for colorimetric biosensing is still a challenge. In this study, to propose a new colorimetric biosensing system, we synthesize three different types of copper cyclic trinuclear unit-based 2D copper-organic frameworks (CuOFs) with covalent structures and light-activable catalytic centers to serve as smart artificial enzymes for highly sensitive and wide-range biocatalytic diagnosis. By varying the light absorption centers, CuOFs with different band structures, light absorption capacity, photoelectron transfer efficiency, and electron-hole pair separation efficiency can be obtained. Of the three covalent CuOFs, tris(4-aminophenyl)amine (Tpa)-Cu3 exhibited the widest light absorption range, the narrowest band gap, the smallest electron transfer barrier, and the best-photoinduced charge separation efficiency, which was conducive to improving the light capture ability and eventually improving the photocatalytic properties. Further tests demonstrated that Tpa-Cu3 exhibited the best peroxidase-like activity under visible light irradiation, which could effectively diagnose the glucose and common antioxidants with a wider detection range and lower detection limit than many previously reported biocatalytic materials. We expect this design will provide new insights into enzyme-like organic framework materials and unique systems for high-sensitive and wide-range colorimetric detection for future biocatalytic applications.