Stuart Bayliss, 20, was one of three survivors of the knife attack Monday afternoon.
Bayliss is a 2015 graduate of Cinco Ranch High School and his mother is a Katy ISD elementary school teacher.
VIDEO: Family of Katy student injured in stabbing talks about recovery
"Very fine young man," Barbara Rozier told Eyewitness News. "He was always very responsible."
Rozier lives across the street from the Bayliss family and caught his parents just as they were heading to Austin Monday afternoon to be with their son.
"All she did was say Stuart was stabbed. We're headed out and that's all she said. She jumped in the car. Her husband was driving and they took off," said Rozier.
Bayliss remained hospitalized Tuesday night.
"We're so grateful to this hospital and the staff and we just want to get him home and get him on his way to recovery," his father told Eyewitness News.
Harrison Brown, a freshman from Graham, Texas, was killed in the attack.
The suspect has been identified as student 21-year-old Kendrex White.
Investigators do not believe he was targeting a group of people, despite rumors that he was going after fraternity members during the attack.
"This was not a conspiracy. This was not a person who had a vendetta against any particular group," UT Police Chief David Carter said.
Police said they have looked into White's history and said they believe he is suffering from mental health issues. Police said they discovered that White was recently involuntarily committed in another city and released.
We've also learned White was recently arrested by campus police for a DWI.
Investigators said White used a "Bowie-style" hunting knife and calmly walked around the plaza.
Video shows him being taken down by police.
"I just see everybody in a panic, in a frenzy, running away, and I look over towards the Gregory Gym area and I just see somebody like passed out on the floor, covered in blood," eyewitness Bryan Ramirez said. "I've never seen anything like this in my life, it's the craziest I've ever seen. I've never seen like horror-stricken faces like that in my life, it was just crazy, it was hectic."
Police said White walked up to a female student, kicked her out of the way and stabbed Brown. White calmly walked away and found another person sitting at a picnic table on the plaza. White stabbed him in the back of the head, police said.
White then walked toward the area of a food truck and stabbed Bayliss and a fourth victim.
He then went to the Jester West dorm where police found him walking toward more students with a knife. Two officers were able to take White down and into custody.
White has been charged with murder.
The UT Counseling and Mental Health Center has extended its hours and UT President Greg Fenves sent a message to the campus community asking for everyone to be "there for one another."
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