Open Mail prefs and click on the Accounts icon in the toolbar. In Account Information uncheck the box at the bottom labeled, "Use only this server." Be sure the box is unchecked in your other account as well. Click on the Composing icon in the toolbar. Look for the drop down menu labeled, "Send new messages from." Select the option to use the account of the selected mailbox. Now when you open a New Message window you will find a drop down menu from which you can select a different server than the default.
The way it should work is automatic. That is if you open Accounts and select your university account then any message you send should be sent automatically using the university's outgoing mail server. You can change servers using the drop down menu but that may not do any good if the other server prevents users from accessing their servers unless they are logged onto their service. Sometimes you can use another server if you configure a userid and password for the outgoing server. But not all services permit that.