Formation of biological filaments via intracellular supramolecular polymerization of proteins or protein/nucleic acid complexes is under programmable and spatiotemporal control to maintain cellular and genomic integrity. Here we devise a bioinspired, catassembly-like isothermal chain-growth approach to copolymerize DNA hairpin tiles (DHTs) into nanofilaments with desirable composition, chain length and function. By designing metastable DNA hairpins with shape-defining intramolecular hydrogen bonds, we generate two types of DHT monomers for copolymerization with high cooperativity and low dispersity indexes. Quantitative single-molecule dissection methods reveal that catalytic opening of a DHT motif harbouring a toehold triggers successive branch migration, which autonomously propagates to form copolymers with alternate tile units. We find that these shape-defined supramolecular nanostructures become substrates for efficient endocytosis by living mammalian cells in a stiffness-dependent manner. Hence, this catassembly-like in-vitro reconstruction approach provides clues for understanding structure-function relationship of biological filaments under physiological and pathological conditions.