A heterogeneous copper-catalyzed A3 coupling reaction of aldehydes, amines, and alkynes for the synthesis of propargylamines and benzofurans has been developed. Here, the modified metal-organic framework MIL-101(Cr)-SB-Cu complex was chosen as the heterogeneous copper catalyst and prepared via post-synthetic modification of amino-functionalized MIL-101(Cr). The structure, morphology, thermal stability, and copper content of the catalyst were determined by FT-IR, PXRD, SEM, TEM, EDX, TGA, XPS, and ICP-OES. The catalyst shows high catalytic activity for the aforementioned reactions under solvent-free reaction conditions. High yields, low catalyst loading, easy catalyst recovery and reusability with not much shrink in catalytic activity, and a good yield of 82% in gram-scale synthesis are some of the benefits of this protocol that drove it towards sustainability.