Greenville city spokeswoman Autumn Barton said nobody had been arrested yet, and that police were trying to determine who was responsible for the attacks.
An argument started inside Skate Safari during a private party and spilled outside, according to Barton. Police received a call around 3 a.m. Saturday about the disturbance, and another caller reported multiple stabbings.
"It started as some type of scuffle and turned into something more severe," said Barton, who adding she had no details on what prompted the dispute. "I'm not sure if it was verbal at first or if it was physical."
Victims were transported to Hunt Regional Medical Center by ambulance and by private vehicles.
Two people were pronounced dead at the hospital, Barton said, and one was a man. Their names were not immediately released.
Several people were hurt, but Barton did not have a specific number. The survivors were hospitalized in varying conditions, Barton said, but she did not elaborate.
"We are trying to gather as much information as possible from witnesses. As soon as they have a clearer picture, they will most likely charge some folks," Barton said.
A message left Saturday at Skate Safari wasn't immediately returned. Greenville is about 50 miles northeast of Dallas.