It was the first time Giffords was removed from the ventilator since last Saturday, when she arrived at University Medical Center after a gunman shot her through the head.
Giffords, 40, remains the only patient in critical condition from the shooting that wounded 12 others. Six more victims were killed in the rampage.
One patient was discharged on Saturday, and two remain hospitalized in good condition.
In the tracheotomy performed on Saturday, doctors replaced a breathing tube running down Giffords' throat with the tube inserted through a hole in her neck, the hospital said in a written statement.
A feeding tube also was inserted into Giffords, a practice not uncommon for patients in intensive care with brain injuries, the hospital said.
Doctors have expressed satisfaction with Giffords' recovery from the bullet wound.
In recent days the congresswoman has opened her eyes and is tracking movement of objects before her, and following simple commands, such as raising fingers and wiggling toes.
Giffords, a Democrat representing Tucson and southern Arizona, was just elected to her third term in the U.S. House of Representatives.
Jared Lee Loughner, a 22-year-old college dropout, is charged as the lone gunman in the rampage.
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