Mitchell was born in Chalfont St. Peter, Buckinghamshire. He graduated from Christ Church, Oxford in 1836.
He illustrated George Robert Gray's 'Genera of Birds', but finding himself too busy with his work for the Zoological Society of London, he employed the German illustrator Joseph Wolf as his assistant on the project.
Mitchell was elected into the Linnean Society in November 1843. He was the first paid secretary of the Zoological Society of London, taking up the post between 10th February 1847 and 6th April 1859, instigating the construction of the first public marine aquarium in the Zoological Gardens, which opened on 22nd May 1853. He was credited with rescuing the zoo financially by publishing attractive images of a few 'star' animals, thus greatly increasing the number of visitors in the late 1840s. He was also a collector and dealer in skins and eggs.
He resigned his post as Secretary of the Zoological Society of London on 6th April 1859, and he became the Aquarium Director of the Jardin d'Acclimatation in Paris, but died on 1st November 1859 after his shot himself only months after taking up the position.
He married Prudence Philips Willes, daughter of Rev Edward Willes of Walcot, near Bath on 30th October 1837.