Assuming your are using POP3, Go into File, Account Settings and double click on the account - then click More Settings and look at the bottom of the Advanced tab.
If the account is set up as imap, mail is synced with the server. You'd need to delete it from Outlook to delete it from the server. There are delete settings in the Advanced tab (use same steps as for POP3). Try changing the settings at the bottom of the dialog. (I have only the bottom purge setting checked, the top one unchecked.)