Hi Katie,
Im running into this issue on my personal account as well. You should still be able to remove tags from a donation, its just not clear that you are doing so. When you click on the little tag icon beside the tag menu, and you see a dropdown of the current tags, clickon an existing one will remove it from the Donation. This is not intention, typically it should highlight or give you some indication that these values are selectable/deselectable.
Also, the 'Manage Tags' button should open a context menu to be able to add/delete/merge existing tags it actually shows up for a quick second before disappearing.
Im going to create a ticket for our development team to look into the issues, and will report back when we have a resolution.
Thanks Katie.
Regards,
Ben