In nanozyme-based assays, increasing enzymatic activity is very desirable for enhancing sensitivity and lowering the detection limit. In this study, novel Mn doped cobalt oxide nanosheets (Mn@Co3O4 NSs) were synthesized by hydrothermal process. The obtained Mn@Co3O4 possessed enhanced dual-enzyme mimetic, oxidase and peroxidase, and can catalytically oxidize of 3, 3′, 5, 5′-tetramethylbenzidine (TMB), to a blue product of oxidized TMB. The enzyme kinetics were well-described mathematically using a common Michaelis-Menten and Lineweaver Burk model. The enzyme kinetics constant (Km) was found to be 0.15 mM, which is relatively low comparing with pure Co3O4 nanosheets (0.35 mM) and natural enzyme HRP (0.434 mM). Therefore, the efficient colorimetric method was achieved for determination of H2O2 and ascorbic acid. The limit of detection (LOD) of H2O2 was 8.0 μM and the linear range was 20–200 μM based on direct turn on of the peroxidase-like activity of Mn@Co3O4. While, for ascorbic acid detection based on turn-off approach, the linearity range for the ascorbic acid was 1–8 μM with LOD of 0.4 μM. Moreover, the colorimetric system exhibited good stability and selectivity toward the detection of ascorbic acid effectively in real samples (vitamin C tablets) with satisfactorily accuracy and precision.