Due process doesn't extend to the battlefield. Having joined the enemy as such a high level operative, Al-Awlaki made himself a target.
Except that Al-Awlaki wasn't on a battlefield. He was sitting a hut somewhere. This is the problem with thinking about terrorism as a military matter. What if Person X, an American citizen, were an AQ operative living in a house in Reno. Can we send in an airstrike to level the house?
Yemen is a battlefield in the effort to fight al Queda. Perhaps if Reno was somehow cut off from the rest of the nation and law enforcement officers, or the military couldn't access the place. Quite unlikely, however.
That's the problem with a "war on terror". The entire planet is one massive battlefield.