It is possible to save a transmog, but it is not possible to delete it. My intuition tells me the way to delete a saved outfit would be to r-click on the outfit from the Saved tab and select 'Remove' or 'Delete' or 'Forget this outfit', but there's nothing. Nor is there any procedure available in the drop downs.

The sets shown in the Saved tab are just a snapshot of a character's saved sets and there is currently no way to delete sets from the tab. To delete a set you need to log into the character and delete the set by clicking on the Rename/Delete button in the saved set dropdown in the dressing room or the transmog vendor.