By mutator phenotype, I mean being more prone to mutations, for example due to mutations in genes involved in DNA repair. I was thinking about exposing the cells to agents that damage DNA (uv light, for example). Compared to normal cells, mutators would be less likely to survive, because they lack the ability to repair damages in the genetic material. To a certain extent, that's the principle of radiotherapy (cancer cells are more suscetible towards radiation). Are there other options? Moreover, is it possible to select the mutators (instead of killing them)?
There are a number of ways to screen for mutator genes. One straightforward approach in bacteria is to take an antibiotic sensitive non-mutator strain, grow it up, and expose to different antibiotics. Cells that survive in the presence of multiple antibiotics have acquired multiple de novo resistance mutations and thus are highly enriched for mutator alleles. Here is one example: Wiegand et al (2008) AAC.