Gary Reagan Sherrill, 51, is being held on a $1 million bond. He allegedly told police he believed his son was a demon and was going to eat him.
Officers went to the Sherrill's home on New Year's Eve and discovered the boy dead after getting a call from the teen's mother, who is Sherrill's ex-wife.
She said Sherrill failed to return their son to her after picking him up a day earlier, and she couldn't reach them.
When Sherrill finally allowed police into his apartment, officers said they found the boy's body in a bedroom with stab wounds and lacerations.
Sgt. Steve Martos, a Phoenix police spokesman, said the department got the call about 10 p.m. on Christmas about Sherrill allegedly making threats and carrying two large sticks.
Police went looking for him, but "they never found him," said Martos, adding that officers took down the information but Sherrill's alleged threats were vague and there wasn't enough information to file a police report.
Some neighbors and friends of Sherrill said his behavior had become increasingly bizarre in the days before Christmas, prompting a 911 call.
"He was saying that somebody was going to get hurt," said Russ Hamilton. "We knew that he just bought an assault rifle, and we were worried that he was going to come over here and start shooting people."
Lynn Hatch, a friend of Sherrill's, said he was a doting father who put his children ahead of his own wants and needs.
Sherrill was once an auditor at a Las Vegas casino and painted homes and laid tile on the side, according to Hatch.
She said she had never seen him act strange, but she last spoke to Sherrill about two months ago.