Two people were critically injured in the attack at the campus of Lone Star College in the Houston city area.
Harris County Sheriff’s Office named the suspect in custody as 20-year-old Dylan Quick.
Dylan Quick was wrestled to the ground by a student, then arrested by police, witnesses said.
The sheriff’s office said in a statement that Dylan Quick had been planning the attack at the campus in Cypress for some time.
Police said he had had fantasies of stabbing people to death since he was in primary school.
Dylan Quick, who was allegedly armed with a razor-type knife, has been charged with aggravated assault.
Police first received an emergency call from the college shortly after 11:00 local time on Tuesday.
Harris County spokesman Thomas Gilliland said the suspect went from “building to building” during the attack.
Diante Cotton, 20, said he saw half a dozen people with injuries to their faces and necks being loaded into ambulances and medical helicopters.
Of the 14 that were injured at the college, two refused medical attention and four were airlifted to hospital.
One student, Michael Chalfan, said the suspect was an “eccentric” type who often wore gloves and was known to carry stuffed animals.
“I’m surprised because he didn’t look like he was hateful to the world,” Michael Chalfan told the Associated Press news agency.
A different Lone Star campus was the site of a shooting in January that left two people wounded.
A 22-year-old man was charged with aggravated assault in that case.
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