I had a fair amount of passive experience with immigration law in the '80s. My understanding from that time, is no native-born American citizen can ever have dual citizenship (unless your parents change your citizenship and you later return to the US.)
If you are born in another country, you can become an American without renouncing your old passport; however, if you are a native-born American and you become a citizen of another country you must renounce your American citizenship.
My question about Al-Awlaki is, did he travel to Yemen with an American passport? Is he presenting himself as an American? If he is, we need to go arrest him and I believe he must go through due process. If however, despite being born in New Mexico, he carries another passport, then the government can declare that he has renounced his citizenship and no longer being an American citizen I imagine can legally be targeted on foreign soil.
Lalo456987 gave the example below of Robert E. Lee losing his citizenship for taking up arms against the US.
I haven't heard what passport this guy has recently been carrying.
Any immigration attorneys have any thoughts?
As per Nickrud's link the following:
POTENTIALLY EXPATRIATING ACTS
Section 349 of the Immigration and Nationality Act (8 U.S.C. 1481), as amended, states that U.S. citizens are subject to loss of citizenship if they perform certain specified acts voluntarily and with the intention to relinquish U.S. citizenship. Briefly stated, these acts include:
1. obtaining naturalization in a foreign state (Sec. 349 (a) (1) INA);
2. taking an oath, affirmation or other formal declaration to a foreign state or its political subdivisions (Sec. 349 (a) (2) INA);
3. entering or serving in the armed forces of a foreign state engaged in hostilities against the U.S. or serving as a commissioned or non-commissioned officer in the armed forces of a foreign state (Sec. 349 (a) (3) INA);
4. accepting employment with a foreign government if (a) one has the nationality of that foreign state or (b) an oath or declaration of allegiance is required in accepting the position (Sec. 349 (a) (4) INA);
5. formally renouncing U.S. citizenship before a U.S. diplomatic or consular officer outside the United States (sec. 349 (a) (5) INA);
6. formally renouncing U.S. citizenship within the U.S. (but only under strict, narrow statutory conditions) (Sec. 349 (a) (6) INA);
7. conviction for an act of treason (Sec. 349 (a) (7) INA).
Looking at section 2, the government is free to renounce his citizenship for him. I think they may want to do this before they take action against him.