SARS-CoV-2 main protease (M^pro) is one of the most extensively exploited drug targets for COVID-19. Structurally disparate compounds have been reported as M^pro inhibitors, raising the question of their target specificity. To elucidate the target specificity and the cellular target engagement of the claimed M^pro inhibitors, we systematically characterize their mechanism of action using the cell-free FRET assay, the thermal shift-binding assay, the cell lysate Protease-Glo luciferase assay, and the cell-based FlipGFP assay. Collectively, our results have shown that majority of the M^pro inhibitors identified from drug repurposing including ebselen, carmofur, disulfiram, and shikonin are promiscuous cysteine inhibitors that are not specific to M^pro, while chloroquine, oxytetracycline, montelukast, candesartan, and dipyridamole do not inhibit M^pro in any of the assays tested. Overall, our study highlights the need of stringent hit validation at the early stage of drug discovery.