Superintendent of police P Sudhakar said Tushar Kanti Das of BSF 64 Battalion had spotted the minitruck at Gaighata in the morning and had given it a chase on a cycle along with a local.
He was hit fatally by the fleeing truck and was rushed to a local hospital, which declared him brought dead.
The truck also hit against a wayside shop while speeding away and the driver jumped down and escaped. The helper was caught by the locals and handed over to the police.
The truck with four cows was seized by the police, Mr Sudhakar added.