Kenneth E. Winter, 46, of Franklinville, turned himself in Wednesday after a judge issued a warrant for his arrest because of the incident, The Buffalo (N.Y.) News reported.
Winter was charged with two counts of third-degree menacing and disorderly conduct and was released with an appearance ticket.
Police said the man's son, a Franklinville High School student, was in a match with a 17-year-old wrestler from Ichabod Crane High School of Valatie Friday at Pine Valley Junior-Senior High School.
"The father was upset over the officiating," said State Police Sgt. Tom Kelly. "He felt his son was being roughed up, so he ran out to the mat and stopped the match."
Winter then allegedly told the Valatie teen he would break his neck and kill him, police said.
The man was removed from the gym, but later ran into the teen in the lobby.
An off-duty trooper at the event happened to hear Winter threaten the boy again, Kelly said. Winter also threatened the trooper, who advised him to leave the gym area.
"These are usually very nice, well attended events," said Cathy Fabiatos, principal of Pine Valley Junior-Senior High School. "It's unfortunate that something like this had to happen."