Swaroop was born in Kashmir, India. His father was a teacher and palmist, and his mother was a homemaker. The family moved to Ajmer in the Rajasthan state. There he studied biology before moving to Pune in the Maharashtra state, where he studied film directing. He had a brief stint at the Indian Space Research Organisation, where he used Russian fairytales to teach science to children. Following this, he attended filmmaking classes in a remote village in Maharashtra.

Swaroop is best known for directing Om-Dar-Ba-Dar (1988) and Rangbhoomi, for which he has received several awards.