The only strategy close to your suggested description is based on FUCCI sensors.
Fluorescent markers designed so that their presence informs of specific stages of the cell cycle, in principle without disrupting or perturbing cell progression.
So, although there is not a physical clean-up of pure cell sub-populations, these can be tracked by the abundance of these markers and even isolated by FACS.
I guess the issue of developing something selectively "lethal" (which does exist in the context of certain plasmids transformed in E.coli) lies partly in being able to retrieve those surviving cells in a timely fashion so that being halted at that particular stage is not detrimental. It does sound as an interesting analogy to Sanger Sequencing where 4 different terminators of each of the 4 bases render truncated fragments easily readable. In principle within the context you suggest, a single cycle would be allowed post genetic manipulation (eventual silencing of such genetic modification as representing an undesirable weight for the cell would be expected otherwise). As progression through each phase varies substantially in time, the idea in itself would require substantial refinement, and most likely the use of a conditional expression system. In this way a mix population transfected with the specific set of markers could be triggered for expression at a given time and then monitored for negative selection.
Commonly though, chemical synchronisation or perhaps more physiologically relevant methods of separation like elutriation, aim at enriching cell populations at specific stages of cell division. Mitotic cells are particularly problematic being rather scarce at any given time within an unperturbed population of growing cells. Mitotic shake-off followed by addition of hypotonic solutions have been suggested as methods of mitotic retrieval but yield is comprehensibly low.