In the field of nucleic acid amplification assays, developing enzyme-free, easy-to-use, and highly sensitive amplification approaches remains a challenge. In this work, we synthesized a heterogeneous Cu2O nanocatalyst (hnCu2O) with different particle sizes and shapes, which was used for developing enzyme- and label-free nucleic acid amplification methods based on the nucleic acid-templated azide–alkyne cycloaddition (AAC) reaction catalyzed by hnCu2O. The hnCu2O exhibited size- and shape-dependent catalytic activity, with smaller sizes and spherical-like shapes exhibiting superior activity. Spherical-like hnCu2O (61 ± 8 nm) not only achieved a ligation yield of up to 84.2 ± 3.9 % in 3 min but also exhibited faster kinetics in the nucleic acid-templated hnCu2O-catalyzed AAC reaction, with a high reaction rate of 0.65 min−1 and a half-life of 1.07 ± 0.09 min. Based on this result, we developed nucleic acid-templated click ligation linear amplification reaction (NA-CLLAR) and nucleic acid-templated click ligation exponential amplification reaction (NA-CLEAR) approach. By combining the recognition (complementary to the target sequence) and signal output (split G-quadruplex sequence) elements into a DNA probe, the NA-CLLAR and NA-CLEAR fluorescence assays achieved highly specific detection of target nucleic acids, with a detection limit of 2.8 aM based on G-quadruplex-enhanced fluorescence. This work is a valuable reference and will inspire researchers to design enzyme-free nucleic acid signal amplification strategies by developing different types of Cu(I) catalysts with improved catalytic activity.