First, the Confrontation Clause isn't a shield meant to provide blanket protection from the use of force prior to a full trial. If it was, the police wouldn't be able to use force --- ever --- to deal with violent crimes in progress.

Second, Al-Awlaki (I assume this is who we're talking about) wasn't executed; he was assassinated. His killing was extrajudicial, a military action and not a law enforcement action. If that's disquieting to you, join the club, and consider whether the problem once again stems to the fact that the USG formally declared war on an organization rather than a state for the first time in its history.

Also worth knowing: Al-Awlaki's killing wasn't unprecedented. US citizens, believed (probably correctly) to be aiding and fighting alongside the Axis powers, were targeted and killed during World War II by US troops.