Why Can't This Happen In The U.S.?

From the El Paso Times:A woman wanted in connection with the 2010 slayings of three people with ties to the U.S. Consulate was arrested Friday by the U.S. Marshals Service.
April Cardoza, 24, of El Paso, was wanted on a federal arrest warrant charging racketeering activities, including multiple instances of violent crimes.
The U.S. marshals and several U.S. law enforcement agencies worked with Mexican officials, who found Cardoza in Juárez on Thursday.
Cardoza was found in the home of Ricardo "Nano" Zuniga who was arrested June 6 and extradited to the U.S. to face captial murder charges in connection with a double homicide in 2009.
Cardoza was living as an undocumented immigrant in Mexico and was deported from Mexico and turned over to U.S. officials Friday at the Paso del Norte bridge.
El Pasoans Lesley Enriquez Redelfs, an employee of the U.S. Consulate in Juárez, and her husband, El Paso County Detention Officer Arthur Redelfs. Their young daughter survived the shooting.
 http://www.elpasotimes.com/ci_20917808/fugitive-u-s-consulate-slayings-found-juarez?source=most_viewed
And if an illegal immigrant wanted for a crime in Mexico or elsewhere is found in the U.S., they may be arrested or not, sent to a jail and then given a lawyer who will demand a trial and the person won't be deported back to Mexico or other country for months or years, if ever.
But when an illegal immigrant is found in Mexico, they are kicked out immediately.
Why can't we do this in the U.S.?