Mitchell was born in Melbourne. Her mother is a model-turned-fashion-designer and her father is a filmmaker; the couple divorced when she was young. Her first name Radha (Sanskrit राधा ) stems from the Hare Krishna faith. The other parts of her name Rani (रानी – queen) and Ananda (आनन्द – joy) also come from similar origins. She credits her name as being 'a creative byproduct' of her mother's experiences in India during the 1970s. She attended St Michael's Grammar School in St Kilda and graduated in 1992.