You can’t permanently delete a campaign on the AdEx platform, but you can "archive" it, which will hide it from your dashboard. If needed, you can still access the campaign through the Archive, which can be accessed through the button in the upper right corner of the Dashboard.
Archiving a campaign is only available for campaigns that have ended; Active or Paused campaigns cannot be archived. Archiving a campaign is done through the three dots in the action section, as shown below: