Two-dimensional molybdenum disulfide (2D-MoS2)-supported single atom nanomaterials with enhanced enzyme-like activities are potential substitutes for natural enzymes due to their huge specific surface areas, ease of decoration, high catalytic activity and high catalytic stability. However, their catalytic mechanism remains unclear, making the rational design of nanozymes difficult to achieve. Herein, the mechanisms have been explored to enhance the peroxidase-like activity of MoS2 for H2O2 decomposition. Global neutral network (G-NN) potentials were constructed to accurately and quickly illustrate the mechanisms of MoS2 catalysts and their surface modifications. The high peroxidase-like activity of the MoS2-supported Cu single atom catalyst with sulfur vacancy (Cu@MoS2-Vs) in acidic conditions was systematically evaluated using the trained G-NN potential and density functional theory (DFT), as well as experimental validation. Further analysis of the geometric and electronic properties of pivotal stationary structures revealed the enhanced electron transfer process for high catalytic performance with the modulation of the Cu single atom loading, sulfur vacancy engineering and the surrounding acidic and alkaline environment regulation on the MoS2 basal plane. The results also showed that Cu@MoS2-Vs in an acidic environment exhibited the highest peroxidase-like activity. This work is expected to provide broad implications for the rational design of substrate-supported single-atom catalysts with superior performance and lower cost by surface modification and acidic and alkaline environment regulation.