Fe3O4@Cu/C and Fe3O4@CuO composites were achieved using nanoparticle-encapsulated MOFs Fe3O4@HKUST-1 as both a precursor and a self-sacrificing template. Fe3O4@HKUST-1 was thermally converted into magnetic Fe3O4@Cu/C and Fe3O4@CuO composites in different atmosphere (N-2 and air). The resulting composites not only kept superparamagnetic characteristics, but also exhibited improved peroxidase-like catalytic activity and high stability when compared to the precursor Fe3O4@HKUST-1. The morphology, crystal structure, magnetic and porous properties of Fe3O4@Cu/C and Fe3O4@CuO composites were characterized, and the kinetics parameters and the influence factors on the peroxidase-mimicking activity such as temperature, pH and H2O2 concentration were evaluated. On account of the excellent peroxidase-like activity, the as-prepared Fe3O4@Cu/C and Fe3O4@CuO composites were successfully used for the catalytic removal of methylene blue (MB) dye with H2O2 oxidant. This work provides an effective way to fabricate highly reactive MOFs-derived biomimetic catalysts, which have potential applications in bioassays and pollutant degradation. Graphic Fe3O4@Cu/C and Fe3O4@CuO composites were achieved using Fe3O4 nanoparticle-encapsulated HKUST-1 as self-sacrificial templates and demonstrated excellent peroxidase-like activity.