We present a detailed theoretical analysis of the reaction mechanism of proteolysis catalyzed by the main protease of SARS-CoV-2. Using multiscale simulation methods, we have characterized the interactions established by a peptidic substrate in the active site, and then we have explored the free energy landscape associated with the acylation and deacylation steps of the proteolysis reaction, characterizing the transition states of the process. Our mechanistic proposals can explain most of the experimental observations made on the highly similar ortholog protease of SARS-CoV. We point to some key interactions that may facilitate the acylation process and thus can be crucial in the design of more specific and efficient inhibitors of the main protease activity. In particular, from our results, the P1' residue can be a key factor to improve the thermodynamics and kinetics of the inhibition process.