Knives and other sharp utensils used to cut or grate, which are designated for meat or dairy, should L’Chatchilah not be used to cut [even cold, non sharp] parve foods that will be used at a meal of the opposite class. (See Shulchan Aruch Yoreh Deah Siman 96:5 and Kaf HaChaim Yoreh Deah Siman 96:51 and 52.) However, if they were totally clean and 24 hours have passed since their last use, the [cold, non sharp] item that was cut retains its parve status and may B’dieved be used at a meal of the opposite class than the utensil.
In general, when cutting, grating or blending different foods, it is always prudent to cut a Parve food last (e.g. Challah or a hardboiled egg) as doing so will ensure that any minute food particles that may have been left on the cutting device will be absorbed into the Parve food and not be present next time it is used. (This is in addition to the thorough cleaning of the knife, as an extra precaution) (See Darchei Teshuva Yoreh Deah Siman 96:56).