To delete a client from a particular tag, you will need to go to the client page. When on the client page, choose the client or clients you want to assign or unassign to a tag.
You will be able to select the tag (1) you want to make the changes to along with being able to do multiple clients (2) at the same time.
Find the client you'd like to remove and click on the X next to their name. Click Assign to Tag and they will be removed from the tag.