...there is an option to leave the message on the server. In Mail 9 that option is in Mail > Preferences > Accounts > Advanced.
You've got
that option backwards.
Edit: That said, I recently read somewhere that Apple removed the option to delete mail from your server in OS X 10.11.2, and, indeed, the option I depicted seems not to be working, although I can still delete emails from my server via control-clicking on Mail > Sidebar > Inbox > Get Account Info.