Genetic information should be accurately transmitted from cell to cell; conversely, the adaptation in evolution and disease is fueled by mutations. In the case of cancer development, multiple genetic changes happen in somatic diploid cells. Most classic studies of the molecular mechanisms of mutagenesis have been performed in haploids. We demonstrate that the parameters of the mutation process are different in diploid cell populations. The genomes of drug-resistant mutants induced in yeast diploids by base analog 6-hydroxylaminopurine (HAP) or AID/APOBEC cytosine deaminase PmCDA1 from lamprey carried a stunning load of thousands of unselected mutations. Haploid mutants contained almost an order of magnitude fewer mutations. To explain this, we propose that the distribution of induced mutation rates in the cell population is uneven. The mutants in diploids with coincidental mutations in the two copies of the reporter gene arise from a fraction of cells that are transiently hypersensitive to the mutagenic action of a given mutagen. The progeny of such cells were never recovered in haploids due to the lethality caused by the inactivation of single-copy essential genes in cells with too many induced mutations. In diploid cells, the progeny of hypersensitive cells survived, but their genomes were saturated by heterozygous mutations. The reason for the hypermutability of cells could be transient faults of the mutation prevention pathways, like sanitization of nucleotide pools for HAP or an elevated expression of the PmCDA1 gene or the temporary inability of the destruction of the deaminase. The hypothesis on spikes of mutability may explain the sudden acquisition of multiple mutational changes during evolution and carcinogenesis.