Cleavage of the C–N bond of a secondary amide could provide alternative access to primary amides; however, this strategy remains challenging due to oxidation resistance of the amide. Herein, we employed the cobalt(II)/Oxone catalytic system, one of the advanced oxidation processes (AOPs), to make it available to break the strong C–N bond of various secondary (sulfon)amides, especially those bearing electron-poor or ortho-substituted N-arenes, en route to desirable primary (sulfon)amides. Control experiments showed that it was probably not the generally-considered persulfate anion radical in the cobalt/peroxymonosulfate (Co/PMS) system but the proposed high-valent cobalt-oxo intermediate that should be the major active species for the initial N–H oxidation of N-aryl amides. In the case of N-alkylated secondary amides, the α-C–H bond, rather than the N–H bond, should be oxidized first by both the reactive radicals and high-valent cobalt-oxo species. This work not only establishes an efficient method for removing the N-substituents of secondary amides at low cost, with readily available and eco-friendly reagents, but also demonstrates further synthetic application and provides more insight into intermediates for metal-based AOPs in environmental remediation.