There is currently no way to "bulk clear" multiple entry fields at the Project Level. Here's the example use case we ran into where this was needed - we needed to update the Resource Managers on a large number of projects, but the projects were originally configured very close to the 30-person limit.
Through bulk editing to project fields, you can only ADD things (you can't take anything away). When we attempted to bulk change the resource manager list, we hit the 30-person limit. As a result, we had to change each project by hand.
The easiest way to do this was through a report (rather than clicking into each project), but on the scale we operate on, this still took a tremendous amount of manual time.