Obtaining random homozygous mutants in mammalian cells for forward genetic studies has always been problematic due to the diploid genome. With one mutation per cell, only one allele of an autosomal gene can be disrupted, and the resulting heterozygous mutant is unlikely to display a phenotype. In cells with a genetic background deficient for the Bloom's syndrome helicase, such heterozygous mutants segregate homozygous daughter cells at a low frequency due to an elevated rate of crossover following mitotic recombination between homologous chromosomes. We constructed DNA vectors that are selectable based on their copy number and used these to isolate these rare homozygous mutant cells independent of their phenotype. We use the piggyBac transposon to limit the initial mutagenesis to one copy per cell, and select for cells that have increased the transposon copy number to two or more. This yields homozygous mutants with two allelic mutations, but also cells that have duplicated the mutant chromosome and become aneuploid during culture. On average, 26% of the copy number gain events occur by the mitotic recombination pathway. We obtained homozygous cells from 40% of the heterozygous mutants tested. This method can provide homozygous mammalian loss-of-function mutants for forward genetic applications.