The implementation of heterogeneous catalysts in advanced organic synthesis provides basis for the sustainable and cost-effective preparation of pharmaceuticals, agrochemicals, and other structurally complex molecules. Crucial for such applications is the design of appropriate catalytic materials with high selectivity and functional group compatibility. Although many homogeneous catalysts are well known for this purpose, heterogeneous ones, specifically those based on non-noble metals, are scarce. Here, we present the preparation and wide-ranging applications of a specific atomically dispersed copper catalyst for highly selective carbene insertion reactions of diazo compounds with alcohols, phenols, amines, thiols, and N-heterocycles. The optimal catalyst (Cu-NC/Al2O3) contains Al2O3-supported copper-based single atoms coordinated with nitrogen species, which can be conveniently prepared by the pyrolysis of Cu-MOF-303. The resulting catalyst allows for the selective formation of C–O, C–N, and C–C bonds in functionalized and structurally diverse molecules (e.g., complex natural products and drugs), including highly sensitive alkynes and azides.