If your account connects using POP, then deleting server copies when you download messages is the default behaviour, unless you specifically change it by setting the checkbox "Leave a copy on server".This can be found under Account Settings.

If your account uses IMAP then it will by its nature leave copies on the server. If you want to clear the server, move the messages you want to keep to the Local Folders account in Thunderbird. Doing this will erase the server copies. For messages you don't want to keep, just delete them in Thunderbird. IMAP synchronization will delete the server copies too.