I’m not sure if I understand your case correctly but the “cancel removal” button (the last in that toolbar) has no effect on peat cutting. Maybe you misclicked and used the “remove structures” button. This one indeed removes peat cutting spots.
If you remove it before the laborer chipped away the sod, then nothing happens. But after the spot was opened, you should not remove it before the peatcutter finished it. Because then the spot is gone without yield and can’t be placed again. Maybe this happened.