Cell proliferation is required for tissue regeneration, yet the dynamics of proliferation during regeneration are not well understood. Here we investigated the proliferation of eye and leg regeneration in fragments of Drosophila imaginal discs. Using twin spot clones, we followed the proliferation and fates of sister cells arising from the same mother cell in the regeneration blastema. We show that the mother cell gives rise to two sisters that participate equally in regeneration. However, when cells switch disc identity and transdetermine to another fate, they fail to turn off the cell cycle and continue dividing long after regeneration is complete. We further demonstrate that the regeneration blastema moves as a sweep of proliferation, in which cells are displaced. Our results suggest that regenerating cells stop dividing once the missing parts are formed, but if they undergo a switch in cell fate, the proliferation clock is reset.