Supporting files can be deleted from a build by navigating to the Test Coverage primary tab, and then to the Builds secondary tab. In the specific build's details window, click on the supporting files icon in the right side vertical menu. To delete a supporting file, click on the vertical menu of the specific file. From the drop down, choose Delete.
Users will need view and edit permissions in the test coverage module to perform this action. Depending on the settings of a users project permissions, users may be able to view all project builds or just a subset of them. Project owners manage the permissions for project members.