New conjugates of substituted 1,2,3-triazoles linked to 1,2,4-triazoles were synthesized starting from the appropriate S-propargylated 1,2,4-triazoles 7 and 8. Ligation of 1,2,4-triazoles to the 1,2,3-triazole core was performed through Cu(I)-catalyzed cycloaddition of 1,2,4-triazole-based alkyne side chain 7 and/or 8 with several un/functionalized alkyl- and/or aryl-substituted azides 9-15 to afford the desired 1,4-disubstituted 1,2,3-triazoles 16-27, using both classical and microwave methods. After their spectroscopic characterization (infrared, 1H, 13C nuclear magnetic resonance, and elemental analyses), an anticancer screening was carried out against some cancer cell lines including human colon carcinoma (Caco-2 and HCT116), human cervical carcinoma (HeLa), and human breast adenocarcinoma (MCF-7). The outcomes of this exploration revealed that compounds 17, 22, and 25 had a significant anticancer activity against MCF-7 and Caco-2 cancer cell lines with IC50 values of 0.31 and 4.98 μM, respectively, in relation to the standard reference drug, doxorubicin. Enzyme-docking examination was executed onto cyclin-dependent kinase 2; a promising aim for cancer medication. Synthesized compounds acquiring highest potency showcased superior interactions with the active site residue of the target protein and exhibited minimum binding energy. Finally, the density functional theory (DFT) calculations were carried out to confirm the outcomes of the molecular docking and the experimental findings. The chemical reactivity descriptors such as softness (δ), global hardness (η), electronegativity (χ), and electrophilicity were calculated from the levels of the predicted frontier molecular orbitals and their energy gap. The DFT results and the molecular docking calculation results explained the activity of the most expectedly active compounds 17, 22, and 25.