Officers found his mother's headless body and the hacksaw inside the Warriners' unit.
Her head wasn't found in the apartment and Jones, citing the ongoing investigation, declined to say whether it had been located.
Authorities believe Sarah Warriner had been dead for at least two days before her body was found.
Days earlier, she had taken her son to a Denton hospital after he used a razor to cut his arms, the affidavit said.
A nurse called security when Isaac Warriner threatened to kill his mother and himself.
Police eventually were called, but he fled the hospital before officers arrived.
Isaac Warriner was spotted in his mother's car on May 6 and led police on a chase up Interstate 35 into Oklahoma, where he was arrested and held before being returned Thursday to Denton.
Online jail records didn't indicate whether he had a lawyer.
His father, Kenneth Warriner, told the Fort Worth Star-Telegram this month that his son suffered a mental breakdown a few months ago.
"She had allowed him to stay with her after his last rehabilitation stay," Kenneth Warriner said of his ex-wife.
"He was prescribed psychotic drugs to try and help, but that didn't seem to work."