Enzymes fold into unique three-dimensional structures to distribute their reactive amino acid residues, but environmental changes can disrupt their essential folding and lead to irreversible activity loss. The de novo synthesis of enzyme-like active sites is challenging due to the difficulty of replicating the spatial arrangement of functional groups. Here, we present a supramolecular mimetic enzyme formed by self-assembling nucleotides with fluorenylmethyloxycarbonyl (Fmoc)-modified amino acids and copper. This catalyst exhibits catalytic functions akin those of copper cluster-dependent oxidases, and catalytic performance surpasses to date-reported artificial complexes. Our experimental and theoretical results reveal the crucial role of periodic arrangement of amino acid components, enabled by fluorenyl stacking, in forming oxidase-mimetic copper clusters. Nucleotides provide coordination atoms that enhance copper activity by facilitating the formation of a copper-peroxide intermediate. The catalyst shows thermophilic behavior, remaining active up to 95 °C in an aqueous environment. These findings may aid the design of advanced biomimetic catalysts and offer insights into primordial redox enzymes.