Mitra was born in Paddington, London, England, the daughter of Nora Downey and Anthony Mitra, a cosmetic surgeon. She has an older and a younger brother. Her father is of Bengali Indian and English descent, and her mother is Irish. In 1984, when Mitra was eight, her parents divorced, and she was sent to boarding school. She spent several years at two different schools, including Roedean, but Mitra claims she was eventually expelled from both of them.
Mitra's first main role came as Scott Wolf's illicit love interest on La vie à cinq (1994). In 2000, Mitra had a small, key role in the film Hollow man - L'homme sans ombre (2000), as the rape victim of Kevin Bacon, an incident that drives his character insane. She had a main role in the medical drama Gideon's Crossing (2000), as "Dr. Alejandra Ollie Klein". Mitra then had roles in Ali G (2002); Fashion victime (2002); Deux en un (2003), and leading roles in Highwaymen - La poursuite infernale (2004) and Spartacus (2004). Mitra appeared in the final season of The practice: Bobby Donnell & associés (1997) as "Tara Wilson", and continued that role into its spin-off Boston Justice (2004), but left not long into the second season. In 2005, Mitra played the role of "Kit McGraw" during Season 3 of Nip/Tuck (2003). Mitra then went on to appear in Skinwalkers (2006), Le nombre 23 (2007) and Shooter, tireur d'élite (2007). In 2008, Mitra starred in the lead role of the science fiction/action film Doomsday (2008) as "Major Eden Sinclair", and, in 2009, went on to star in Underworld 3 - Le soulèvement des Lycans (2009) as "Sonja", the daughter of the powerful vampire elder, "Viktor" (played by Bill Nighy).
Mitra appeared as the live action model for "Lara Croft", the lead character in Eidos Interactive's Tomb Raider video game series. She was ranked #46 on the Maxim Hot 100 Women of 2001.
