Giffords had an operation Saturday to replace the breathing tube with a tracheotomy tube in her windpipe. That allows her to breathe better and frees her from the ventilator.
Though Giffords had been breathing on her own since she was shot in the head Jan. 8, doctors had left the breathing tube in as a precaution.
Giffords' doctors have said they should be able to evaluate her ability to speak once the breathing tube is out.
Special Section: Tragedy in Tucson
Doctors also inserted a feeding tube. These procedures are not out of the ordinary for brain-injured patients.
Giffords was shot in the head Saturday in an attack in Tucson that wounded 12 others and killed six people. She remains in critical condition.
"Her recovery continues as planned," the hospital said in a statement.
Her husband, astronaut Mark Kelly, has remained by her bedside.
One patient was discharged Saturday while two others remain in good condition.