Rasikul Mondal was attacked by the smugglers and received serious injuries in his right eye when he chased them as they were ferrying a large number of cattle.
Mondal was first taken to a sub-divisional hospital and later to R G Kar Hospital in Kolkata where he was declared brought dead, the official said.
A commanding officer level flag meeting was held today with Border Guard Bangladesh (BGB) in which BSF requested it to arrest the culprit.
The BSF HQ has also taken the incident seriously and contacted BGB HQ at Dhaka to lodge a protest, the official said.