A study of ion sculpting dynamics in SiO2 and SiN using periodically pulsed ion beams reveals material transport that depends strongly on the time structure of the pulsed beams. It is found that significant nanoscale matter transport can occur over second long time scales after the ion beam has been extinguished. A simple phenomenological model described the dynamics of ion beam sculpting in terms of two material time scales. The model accounts for the surprising observation of enhanced matter transport affected by pulsed ion beams over continuous ion beam exposure.