The incident happened at their house in North Dinajpur's Karandighi on Tuesday night when the youth slit the throat of the 80-year-old man with the dagger. The youth also attacked the girl, her grandmother and a child of the family with a dagger.
They were admitted to super-speciality hospital in Raiganj where the child also died later.
Police said that a man named Ali Shah, who had killed the octogenarian at Gardankata village has been arrested.
Police told media "Around 10am yesterday (Tuesday), he forcibly entered her room and tried to rape her. As she raised the alarm, family members rushed for help. Shah was carrying a dagger and attacked all those who came to save her. We have filed a police complaint against Shah who ran away."