1,2,3-triazole skeleton is a privileged building block for the discovery of new promising anticancer agents. In this report, new 1,4-disubstituted 1,2,3-triazoles with the bioisoster triazole moiety were straightforwardly prepared under copper-catalyzed azide-alkyne [3+2] cycloaddition reactions (CuAAC) regime using a variety of both functional organic azides and terminal alkynes. The resulting functional 1,4-disubstituted 1,2,3-triazole compounds were fully characterized and subsequently tested for their antiproliferative activity against four different cancer cell lines. The cytotoxicity tests carried out with these 1,2,3-triazole derivatives show average IC50 values ranging from 15 to 50 μM by comparison with the standard reference drug, namely doxorubicin. The phosphonate 1,2,3-triazole derivative was found to exhibit the best antiproliferative activity among the studied compounds against the HT-1080 cell lines. It was chosen to evaluate its mode of action in these cancer cell lines. The cell cycle study showed that the phosphonate derivative, compound 8, is the most active inhibitor of the cell cycle at the G0/G1 phase, inducing apoptosis independently of Caspase-3 and causing an increase in the mitochondrial membrane potential (ΔΨm) in the HT-1080 cell lines. Molecular docking studies of this phosphonate derivative into the MMP-2 and MMP-9 metalloproteinases receptors demonstrated the relevance of triazole scaffolds and the pendant phosphonate group in establishing -anion, -alkyl and hydrogen bonding type interactions with residual components in the active MMP pocket.