The incident took place at Beheramal village last night over some past dispute.
The victims were identified as Pramod Bhoi (70), his daughter Bishnupriya Bhoi (50) and minor grand daughter Babita (17), police said.
Bhoi's neighbour Neela Pradhan allegedly hacked them to death using an axe. Police arrested Pradhan after he himself surrendered at the police station.
Pradhan also surrendered the weapon used in the crime.
"Two persons died on the spot while the minor girl died at the hospital. Preliminary investigation reveals that the family was attacked by thier neighbour over some past dispute," said Birmaharajpur Sub-Divisional Police Officer (SDPO), Prasanna Kumar Biswal.