Well, as someone who has worked most of his career in public institutions, I assure you UT is going to follow some form of due process in this situation. Now I realize Beard has a contract with specific language, but UT also has it's own internal policies and processes they must follow. Most of the time when an institution gets itself in trouble it is because they didn't follow their own policies and processes.
I promise you UT has an employment policy and process for this, even for a coach with contract language stated as posted above. And I guarantee you they will follow that process to the letter. It's not the same "due process" the federal government mandates they have to do with students and even with faculty, but they do have a due process procedure they most certainly are going to follow to the letter (or be prepared to pay him that which they don't want, and shouldn't have, to pay him).