The nephew of New York Giants President John Mara rang in the new year by nearly beating a man to death in a college party brawl in Connecticut, authorities said yesterday. The younger Mara, also named John, is 22, lives in Mount Kisco, and turned himself in Friday to Fairfield, Conn. police. Mara allegedly bashed a man in the head with a bottle during a New Year's Eve argument at a Fairfield University party held in a luxury beach house in a chi-chi section of the town. A source said doctors told the victim that if he hadn’t gone to the hospital, “he would have been dead.” “There were some side effects,” the source said. “They had to operate.”