The incident occurred under the Basrehar Police Station area here.
Deepkant attacked his 50-year-old aunt Kamla Devi, killing her on the spot. His mother Javitri Devi (55) was killed when she tried to save her, Additional Superintendent of Police Jitendra Srivastava said.
He attacked his father Nahar Singh (60) when he returned home, the officer said, adding that by the time neighbours reached the spot, they had died.
They overpowered him and handed him over to the police, the ASP said.
Deepkant was unemployed and had married about seven months ago. His family used to put pressure on him to take up some work, the officer said.