There is an urgent need for vaccines and antiviral drugs to combat the COVID-19 pandemic. Encouraging progress has been made in developing antivirals targeting SARS-CoV-2, the etiological agent of COVID-19. Among the drug targets being investigated, the viral main protease (Mpro) is one of the most extensively studied drug targets. Mpro is a cysteine protease that hydrolyzes the viral polyprotein at more than 11 sites and it is highly conserved among coronaviruses. In addition, Mpro has a unique substrate preference for glutamine in the P1 position. Taken together, it appears that Mpro inhibitors can achieve both broad-spectrum antiviral activity and a high selectivity index. Structurally diverse compounds have been reported as Mpro inhibitors, with several of which also showed antiviral activity in cell culture. In this study, we investigated the mechanism of action of six previously reported Mpro inhibitors, ebselen, disulfiram, tideglusib, carmofur, shikonin, and PX-12 using a consortium of techniques including FRET-based enzymatic assay, thermal shift assay, native mass spectrometry, cellular antiviral assays, and molecular dynamics simulations. Collectively, the results showed that the inhibition of Mpro by these six compounds is non-specific and the inhibition is abolished or greatly reduced with the addition of reducing reagent DTT. In the absence of DTT, these six compounds not only inhibit Mpro, but also a panel of viral cysteine proteases including SARS-CoV-2 papain-like protease, the 2Apro and 3Cpro from enterovirus A71 (EV-A71) and EV-D68. However, none of the compounds inhibits the viral replication of EV-A71 or EV-D68, suggesting that the enzymatic inhibition potency IC50 values obtained in the absence of DTT cannot be used to faithfully predict their cellular antiviral activity. Overall, we provide compelling evidence suggesting that ebselen, disulfiram, tideglusib, carmofur, shikonin, and PX-12 are non-specific SARS-CoV-2 Mpro inhibitors, and urge the scientific community to be stringent with hit validation.