Mitra was born in his father's hometown of Konnagar, a suburb of Kolkata (then Calcutta) located in the Hooghly District in the Bengal Presidency (present-day West Bengal). He was the third son of Joykrishna Mitra, who was a schoolteacher at the time of Mitra's birth, and Saratkumari, a medical student whose family came from Midnapore. While Mitra's paternal family were orthodox Hindus, his mother's family were adherents of the progressive Brahmo Samaj, and were noted in Midnapore for their advanced outlook. In 1878, Joykrishna Mitra had joined the Brahmo Samaj and married his wife, against the wishes of his family, who responded by severing ties with him. As a consequence, the newly wed couple moved to Saratkumari's hometown of Midnapore, where Joykrishna and his wife had two sons – Satish Kumar and Santosh Kumar – and a daughter before Joykrishna moved his family to Kolkata in 1889; there, he became a schoolteacher. Mitra was born the following year.