Removing an authenticator from your account is pretty easy -- so long as you have the authenticator handy. But if you don't -- like if you've upgraded your smartphone and your mobile authenticator doesn't work anymore -- then you've got a bit more trouble ahead. Usually Blizzard has an online form to help you out of a problem like this, but the form is currently MIA which makes getting help a bit harder.
Blizzard is working to get the page back online, but in the meanwhile, you'll have to resort to contacting customer support directly for help. Customer Support rep Araxom says anyone having trouble removing an authenticator will need to contact support using one of the methods at the bottom of the support page -- which means you can open a ticket, set up a phone callback, or jump into a live chat. None of these methods are instant, but they will wind up getting you the authenticator help you need without too much of a wait.
Just remember to add a new authenticator once you've removed this one -- it's a security feature you won't regret having.