To delete all support files from an IBM Security Access Manager V9.0 appliance, the correct command is 'deleteall' found under the support menu in the Command Line Interface (CLI). This 'deleteall' command is specifically designed to clear out all support-related files in one go, ensuring that no remnants are left behind. Other commands such as 'delete' or 'purge' do not offer the comprehensive clearance of all support files as the 'deleteall' command does.