At approximately 10:13 p.m. Friday, Sione Vaitai, 26, was engaged in a dispute with family members at Mount View Drive in Sandy, Sandy police said.
During the dispute, Vaitai obtained a large knife and assaulted his father and juvenile sister, police said.
Local media report officers responded to the home but Vaitai had already fled the scene. The two victims were transported to local hospitals in critical condition.
Police have not been able to locate Vaitai, who is described as a male Polynesian, 6-feet tall and 300 pounds with dark hair.