Facilely synthesized peroxidase-like nanozymes with high catalytic activity and stability may serve as effective biocatalysts. The present study synthesizes peroxidase-like nanozymes with multinuclear active sites using two-dimensional (2D) metal-organic framework (MOF) nanosheets and evaluates them for their practical applications. A simple method involving a one-pot bottom-up reflux reaction is developed for the mass synthesis of (Cu-S)n MOF 2D nanosheets, significantly increasing production quantity and reducing reaction time compared to traditional autoclave methods. The (Cu-S)n MOF 2D nanosheets with the unique coordination of Cu(I) stabilized in Cu-based MOFs demonstrate impressive activity in mimicking natural peroxidase. The active sites of the peroxidase-like activity of (Cu-S)n MOF 2D nanosheets were predominantly verified as Cu(I) rather than Cu(II) of other Cu-based MOFs. The cost-effective and long-term stability of (Cu-S)n MOF 2D nanosheets make them suitable for practical applications. Furthermore, the inhibition of the peroxidase-like activity of (Cu-S)n MOF nanosheets by glutathione (GSH) could provide a simple strategy for colorimetric detection of GSH against other amino acids. This work remarkably extends the utilization of (Cu-S)n MOF 2D nanosheets in biosensing, revealing the potential for 2D (Cu-S)n MOFs.