Most attempts to target the novel coronavirus SARS-CoV2 are focusing on the main protease (Mpro) 1-9. However, >19,000 missense mutations in the Mpro have already been reported 10. The mutations encompassing 282 amino acid positions and these “hotspots” might change the Mpro structure and activity, potentially rendering novel antivirals and vaccines ineffective. Here we identified 24 mutational “coldspots” that have resisted mutation since the virus was first detected. We compared the structure-function relationship of these coldspots with several SARS-CoV2 Mpro X-ray crystal structures. We found that three coldspot residues (Leu141, Phe185 and Gln192) help to form the active site, while six (Gly2, Arg4, Tyr126, Lys137, Leu141 and Leu286) contribute to dimer formation that is required for Mpro activity. The surface of the dimer interface is more resistant to mutations compared to the active site. Interestingly, 16 coldspots are found in conserved patterns when compared with other coronaviruses. Importantly, several conserved coldpots are available on the surface of the active site and at the dimer interface for targeting. The identification and short list of these coldspots offers a new perspective to target the SARS-CoV2 Mpro while avoiding mutation-based drug resistance.