The copper-catalyzed cycloaddition of alkynes and azides (CuAAC) to give the corresponding 1,4-disubstituted-1,2,3-triazoles is the most successful and leading reaction within the click chemistry regime. Its heterogenization stands out as the innovative strategy to solve its environmental concerns and toxicity issue. In this report, magnetically retrievable activated carbon produced from biomass Persea Americana Nuts was loaded with a catalytically active copper(I) catalyst, resulting into a heterogeneous nanocatalyst, namely Cu-Fe3O4-PAC. This new compound was fully characterized using several techniques such as Powder X-ray diffraction (PXRD), Fourier-transform infrared spectroscopy (FT-IR), Scanning Electron Microscopy (SEM), Energy Dispersive X-ray diffraction (EDX), Brunauer–Emmett–Teller (BET) analysis, and Raman spectroscopy. Cu-Fe3O4-PAC catalyzed the cycloaddition of a variety of substituted terminal alkynes and organic azides in water at room temperature with excellent yields and in a regioselective manner. The hot filtration test demonstrated that no significant leaching of catalytically active copper particles took place during the CuAAC process, a feature that supports the stability of Cu-Fe3O4-PAC and its heterogeneous action way. Cu-Fe3O4-PAC was magnetically separable by applying an external magnetic field and was recyclable up to five runs, with only an 8% decline in its activity after the 5th catalytic test. The hot filtration experiment heavily suggested that the present catalytic system would proceed in a heterogeneous manner in CuAAC. The electronic characteristics, nature of the intermediate complexes, and type of ligand-to-copper bonding interactions were studied by using quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) calculations, which enabled the confirmation of the proposed binuclear mechanism.