The $600 million-a-year trade has flourished over the past four decades and is considered legal by Dhaka.
Roughly every other night, troops armed with bamboo sticks and ropes wade through jute and paddy fields and swim across ponds to chase ageing bovines, and smugglers, headed for markets in Bangladesh.
The crackdown is one of the clearest signs yet of how Indian policies, increasingly influenced by Hindu nationalist ideology, are having an economic impact on neighbouring countries as well as the sizeable Muslim minority at home.
About 2 million head of cattle are smuggled into Bangladesh annually from India.
The $600 million-a-year trade has flourished over the past four decades and is considered legal by Dhaka.
Modi's government, which came to power with the help of the Hindu nationalist Rashtriya Swayamsevak Sangh, wants to put an end to it.
Union Home Minister Rajnath Singh travelled this spring to the frontier with Bangladesh, calling on the Border Security Force to halt cattle smuggling completely so that the 'people of Bangladesh give up eating beef', media reported at the time.
"Killing or smuggling a cow is equivalent to raping a Hindu girl or destroying a Hindu temple," said Jishnu Basu, an RSS spokesman in West Bengal, which shares a 2,216 km (1,375 miles) border with Bangladesh.
BEEF PRICES UP, EXPORTS DOWN
So far this year, BSF soldiers have seized 90,000 cattle and caught 400 Indian and Bangladeshi smugglers.
Bangladeshi traders who operate auctions to facilitate the sale of cattle to slaughter houses, beef processing units, tanneries and bone crushing factories estimate the industry contributed 3 per cent to the country's $190 billion economy.
The hit to GDP from India's policies is not yet known.
But HT Imam, a political adviser to Bangladesh Prime Minister Sheikh Hasina, said there was "absolutely no doubt" that the beef trade and leather industry were suffering.
Syed Hasan Habib of Bengal Meat, Bangladesh's top beef exporter, said it had to cut international orders by 75 per cent.
The company exports 125 tonnes of beef a year to Gulf countries.
He said the price of cows had gone up by 40 per cent over the past six months because of India's move, and they had been forced to close two processing units.
Habib plans to import cows from Nepal, Bhutan and Myanmar to meet domestic demand, but he said Indian cows had better quality meat and raw hide.
Bangladesh Tanners Association president Shaheen Ahmed said 30 of 190 tanneries had suspended work due to lack of hides, and about 4,000 workers were jobless.
A senior official in India's home ministry said Bangladesh should find new sources of beef because India would stick to its stance.
COW PROTECTION FORCE
India is home to 300 million cattle and is the world's largest beef exporter and fifth-biggest consumer.
But since Modi's Bharatiya Janata Party, which is closely linked to the RSS, came to power last year, the rhetoric on cow protection and the beef ban has increased.
Critics say tougher anti-beef laws discriminate against Muslims, Christians and lower-caste Hindus who rely on the cheap meat for protein. Butchers and cattle traders, many of them Muslim, say the push threatens thousands of jobs.
The rhetoric has also emboldened vigilante cow protectors.
"I was chained to a tree and beaten by members of the cow protection force.
"They forced me to recite a Hindu prayer," said Mohammed Tarafdar, who was caught smuggling two calves near the Bangladesh border in April.
"My religion permits me to eat and sell beef, so why should Hindus have a problem?" said Tarafdar, sitting in a crammed prison cell in Basirhat district.
"Some BSF soldiers said they could not understand why they were chasing cows. Some animals are caught and auctioned by the BSF, only to be bought and smuggled again.
Two soldiers were killed by a gang of Bangladeshi smugglers, while three dozen have been injured by the animals.
"It is a wild chase, but not of a kind a soldier appreciates," said Vivek Tyagi, a BSF commander at the Ghojadanga check post.
Image: India is home to 300 million cattle and is the world's largest beef exporter and fifth-biggest consumer. Photograph: Getty Images
(Additional reporting by Sujoy Dhar in Kolkata)
Beef ban and the death of protest
When Hindus ate beef, India was NEVER conquered