There's actually a way to delete teams uploaded to the Server. This method assumes you tried deleting the teams in the teambuilder.
To prevent the PS! server-side team database from automatically syncing your uploaded teams to your teambuilder every time you login to your account on a new browser/device, type /teams into any chat, and click "Manage" -> "Delete team" for every team you don't want to keep synced to the database. Please keep in mind that deleting teams from the database in this fashion will permanently delete them from the database.
I used this method to delete outdated teams I had uploaded on the the Showdown server, and it deleted them without them showing up in the teambuilder again.
Source: typing/rfaq dupe in the Help Chatroom on Pokemon Showdown