Despite the widespread use of nanozyme-based colorimetric assays in biosensing, challenges such as limited catalytic efficiency, inadequate sensitivity to analytes, and insufficient understanding of the structure-activity relationship still persist. Overcoming these hurdles by enhancing the inherent enzyme-like performance of nanozymes using the unique attributes of nanomaterials is still a significant obstacle. Here, we designed and constructed Pd–Cu2O nanocages (Pd–Cu2O NCs) by selectively etching the vertices of the copper octahedra to enhance the peroxidase-like (POD-like) activity of Cu2O nanoparticles. The improved catalytic activity of Pd–Cu2O NCs was attributed to their high specific surface area and abundant catalytic sites. Mechanistic studies revealed that reactive oxygen species (ROS) intermediates (•OH) were generated through the decomposition of H2O2, resulting in POD-like activity of the Pd–Cu2O NCs. The designed Pd–Cu2O NCs can oxidize 3,3′,5,5′-tetramethylbenzidine (TMB) in the presence of H2O2, producing a blue oxidation product (oxTMB). The oxidation reaction was inhibited and led to a significant bleaching of the blue color in the presence of reducing substances isoniazid (INH) and ascorbic acid (AA). Based on these principles, we developed a colorimetric sensing platform for the detection of INH and AA, exhibiting good sensitivity and stability. This work provided a straightforward approach to the structural engineering of nanomaterials and the enhancement of enzyme-mimicking properties.