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.

In 1974, Swaroop graduated from the Film and Television Institute of India. His student work met with unusual international acclaim. He continued with postgraduate studies at the Institute.

Swaroop assisted the director Richard Attenborough in the filming of Gandhi (1982).