Novel one-pot synthesis naphtho2,3-gphthalazine (1a–1k) of Mannich base derivatives can be achieved via grindstone chemistry using a Tel-Cu-NPs (telmisartan-copper nanoparticles) catalyst. This method offers efficient mild reaction conditions and high yields. Tyrosinase inhibitory activity was evaluated for all synthesized compounds, along with analysis of kinetic behavior and molecular docking studies. The synthesized compound, 1c was (IC50 = 11.5 µM) more active than kojic acid (IC50 = 78.0 µM). Lineweaver Burk plots were used to analyze the kinetic behavior of the most active compound 1c, it was reversible and competitive behavior. Compound 1c and kojic acid occurred in the presence of 2-hydroxyketone, which has the same inhibitory mechanism. The molecular docking of compound 1c and the control kojic acid were docked against 2Y9X protein via the Schrodinger Suite. The compound 1c showed a respectable dock score (−5.6 kcal/mol) compared to kojic acid with a dock score of (−5.2 kcal/mol) in the 2Y9X protein. Cytotoxicity activity was also evaluated by using HepG2 (liver), MCF-7 (breast), and HeLa (cervical) cancer cell lines, and high activity for 1c (GI50 = 0.01, 0.03, and 0.04 µM, respectively) against all cell lines was found compared to standard and other compounds. Therefore, this study succeeded in testing a few promising molecules as potential antityrosinase agents.