Two-dimensional (2D) nanomaterials are attractive in catalysis due to their rich accessible active sites. Iron-based metal organic frameworks (MOFs) are promising nanozymes because of their iron center and pore structure. However, it is challenging to obtain iron-based 2D MOF nanozymes due to the coordinated form of iron. Herein, we report a cation substitution strategy to transform an easily obtained Cu(HBTC)(H2O)3 (represented as Cu(HBTC)-1, the product of only two carboxylate groups in 1,3,5-benzenetricarboxylic acid (H3BTC) ligands linked by Cu ions) nanosheet into a 2D Fe-BTC nanosheet, which was characterized by SEM (scanning electron microscopy), AFM (atomic force microscopy), XPS (X-ray photoelectron spectroscopy), FT-IR (Fourier transform infrared spectroscopy), and XRD (X-ray diffraction). The 2D Fe-BTC nanosheet can catalyze TMB (3,3',5,5'-tetramethylbenzidine) oxidation by H2O2, showing its intrinsic peroxidase mimetic characteristic. The catalytic performance of 2D Fe-BTC was superior to those of its template Cu(HBTC)-1 nanosheet and 3D MIL-100(Fe). Their catalytic activities follow the order of 2D Fe-BTC > MIL-100(Fe) > 2D Cu(HBTC)-1. The peroxidase-like activity of 2D Fe-BTC is 77 times that of its template Cu(HBTC)-1, and 2.2 times that of MIL-100(Fe), a well known 3D crystalline form of iron trimesates. The Km values of 2D Fe-BTC for TMB and H2O2 were 0.2610 mM and 0.0334 mM, which were 1.6 and 1.9-fold lower than those of 3D MIL-100(Fe), respectively. The TMB oxidation rate and H2O2 reduction rate at unit mass concentration of the catalyst (Kw) for 2D Fe-BTC were 2.7-72.3 and 1.5-37.9 times those for the previously reported 3D MOF nanozymes, respectively. In terms of the excellent peroxidase mimetic characteristic of 2D Fe-BTC, a sensitive and selective colorimetric biosensing platform for hydrogen peroxide and glucose was developed. The linear ranges are 0.04-30 μM and 0.04-20 μM for H2O2 and glucose, with a low detection limit of 36 nM and 39 nM, respectively. The assay was satisfactorily applied to glucose determination in biological matrices.