Saswata is the son of famous bengali actor Subhendu Chatterjee. In his teens, Saswata would watch a lot of theatre and enact scenes in front of the mirror. His father (late Shubhendu Chatterjee) had no clue what he wanted to do in life. He would pester him about this and that decided to take up acting as profession. Saswata started out in group theatre, acting for Noted actor Jochon Dastidar's Charbak. He was Saswata's mentor. Saswata started his television career with a Hindi serial directed by Saibal Mitra, based on Samaresh Majumdar’s Kaalpurush. He gained popularity by portraying the character of Topshe in a television series directed by Satyajit Ray's son Sandip Ray. His breakthrough role came in Sujoy Ghosh's 2012 blockbuster hindi film, 'Kahaani', where he played a simple looking scary contract killer Bob Biswas. The nation went crazy with his portrayal of the villain and comparisons with the iconic villainous characters - 'Mogambo' and 'Gabbar Singh' were also drawn.