HERRIMAN, Utah—Eight months to the day after his only son, Chandler, killed himself, Kurt Voutaz was in his kitchen eating lunch.

He and his wife, Catherine, had long since ripped the blood-soaked carpet out of Chandler’s bedroom and cleaned the walls and ceiling. It was warm for February, and they had taken the snow tires off the car. They were hoping winter was over.

Suddenly, a police car sped across a footpath in the park behind their house. A couple of teenagers were standing nearby, shouting.

Mr. Voutaz stepped outside to see what was going on. He quickly wished he hadn’t. Just a few yards from his house, a body was lying on the ground. It was Chandler’s friend, Cooper Nagy. Like Chandler, he had shot himself.

Cooper was the fourth high-school student from Herriman to die by suicide since Chandler’s death in June of 2017. Two more would kill themselves by May of 2018, bringing the total to six in less than a year, plus at least one recent graduate.