KOLKATA—Sitting outside a tiny office beneath a colorful portrait of a bull, members of the Bharatiya Janata Party’s Cow Development Cell relive their recent exploits: setting up road blocks, stopping cattle trucks and freeing cows bound for the slaughterhouse.

“We have to do it to save our cow mother,” says Subrata Gupta, head of the state of West Bengal’s branch of the group, an official arm of Prime Minister Narendra Modi’s political party.

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