You're right, they don't actually "remove" donuts, but the mandrels do essentially move them out of the way, like moving the material to the outside; more so if the cases are annealed.
After annealing (as I do after every firing), I've taken pin gauges to measure the amount of "neck tension" and to see what the ID's of the donuts actually are. I've had as much as .002 difference between the ID of the donut opening and the rest of the case neck. After running my mandrel through the necks then the pin gauges to see any changes in the donut ID, there was no obstruction of the pin gauge all the way through for the "neck tension" I was setting. One of the reasons I bought some pin gauges was to find out definitively the size of the donuts before and after various sizing methods.
For necks that haven't been annealed, particularly those that have never been done after several firings, little or no movement of the donut by running a mandrel through the neck is expected due to the amount of springback.