The massive assessment of immune evasion due to viral mutations that increase COVID-19 susceptibility can be computationally facilitated. The adaptive cytotoxic T response is critical during primary infection and the generation of long-term protection. Here, potential HLA class I epitopes in the SARS-CoV-2 proteome were predicted for 2,915 human alleles of 71 families using the netMHCIpan EL algorithm. Allele families showed extreme epitopic differences, underscoring genetic variability of protective capacity between humans. Up to 1,222 epitopes were associated with any of the twelve supertypes, that is, allele clusters covering 90% population. Next, from all mutations identified in ~118,000 viral NCBI isolates, those causing significant epitope score reduction were considered epitope escape mutations. These mutations mainly involved non-conservative substitutions at the second and C-terminal position of the ligand core, or total ligand removal by large recurrent deletions. Escape mutations affected 47% of supertype epitopes, which in 21% of cases concerned isolates from two or more sub-continental areas. Some of these changes were coupled, but never surpassed 15% of evaded epitopes for the same supertype in the same isolate, except for B27. In contrast to most supertypes, eight allele families mostly contained alleles with few SARS-CoV-2 ligands. Isolates harboring cytotoxic escape mutations for these families co-existed geographically within sub-Saharan and Asian populations enriched in these alleles according to the Allele Frequency Net Database. Collectively, our findings indicate that escape mutation events have already occurred for half of HLA class I supertype epitopes. However, it is presently unlikely that, overall, it poses a threat to the global population. In contrast, single and double mutations for susceptible alleles may be associated with viral selective pressure and alarming local outbreaks. The integration of genomic, geographical and immunoinformatic information eases the surveillance of variants potentially affecting the global population, as well as minority subpopulations.