Polymeric nanoparticles with peroxidase-like enzyme mimetic activity were developed by incorporating catalytically active tellurium (Te) functionalities into cross-linked block copolymers. Bis(2-aminophenyl) ditelluride was used as a cross-linker to react with a diblock copolymer bearing pendent activated ester groups to generate of core-cross-linked nanoparticles (DiTe-NP) containing diaryl ditelluride bonds. DiTe-NP nanoparticles exhibit dual redox-responsiveness inherited from the sensitivity of ditelluride to both oxidants and reductants. When DiTe-NP nanoparticles were treated with H2O2, the oxidation of the ditellurides triggered the cleavage of Te-Te bonds to form Te(IV)-associated species. The oxidation-responsiveness endows DiTe-NP nanoparticles with haloperoxidase (HPO)-mimic activity. With NaBr and hydrogen peroxide, they catalyzed the oxidative bromination of phenol red, bromolactonization of 4-pentenoic acid, and bromination of 1,3,5-trimethoxybenzene due to the in-situ generation of hypobromous acid (HOBr) for halogenations. These ditelluride-containing nanoparticles also exhibited glutathione peroxidase (GPx)-like activity and accelerated the reduction of hydroperoxide by a thiol substrate. The cleavage of ditelluride bonds by a thiol substrate leads to the formation of key intermediates in the catalytic cycle of DiTe-NP nanoparticles. DiTe-NP nanoparticles showed enhanced activity for the reduction of hydrophobic cumene peroxide by 4-nitrothiophenol. These dual redox-responsive ditelluridecontaining nanoparticles are promising candidates as peroxidase mimetics to apply as catalysts for green halogenation reactions and decompositions of toxic peroxides.