Without the use of an add-on - disable the signature editing permission for the primary usergroup (so no one can add a new signature), then manually remove the exisiting ones user by user via the ACP.
There may be another way, but that's how I've done it at one site.
As well as Shaun's suggestion to edit the usergroup permission to prevent future changes, the best way to remove the signatures en-masse is to run this query on your XenForo database: