Mitchell was born and brought up in Aberdeen, but came to Newcastle on 24 September 1842, to work in John Coutts' new yard at Walker. He left in 1844 and spent time in London and abroad before returning in 1852 to found his own shipyard on the Tyne.
From 1857, Mitchell built a considerable number of ships for Russia, and in 1862 was invited to Petersburg to superintend the conversion of the shipyards to the building of iron ships. He was decorated with the Imperial Order of St Stanislaus, 2nd class (normal for foreign nationals), and this may be seen in the coat of arms over the door of Jesmond Towers (now the La Sagesse school. In 1871, Mitchell was among those greeting the High Admiral, Grand Duke Constantine at Newcastle Central station, after which the party drove on to Jesmond Towers. The Russian guests had come to visit the Low Walker yard and have a quick tour of the river.
From 1867, Armstrong made an informal agreement with Mitchell to arm his ships, and this turned into a permanent partnership negotiated in 1882. Under this agreement, armoured vessels were to be built at the Armstrong works in Elswick, and other types at Low Walker. The next twenty years saw huge prosperity. In his review of the region's history conducted for the 1970 Durham meeting of the British Association, W.M. Hughes commented that:

It is perhaps hard for us to realise after the years of intervening depression that for sixty years before 1914, the Durham (and Northumberland) pitmen and the shipyard workers of the Tyne and Wear were among the most highly-paid workers in the world outside the USA... The decline into poverty of the inter-war years was from the heights to the depths.

Work included the world's first bulk oil carrier the Gluckhauf, built at Walker, and the spectacular Baikal, a railway ferry sent in 7200 pieces to be reassembled at Lake Baikal as part of the Trans-Siberian railway. Mitchell's friend Henry F. Swan did much work in the icebreaker field. and when a powerful Baltic icebreaker was proposed, it was to Swan that Admiral Makarov turned for the building of the renowned Yermak.
In 1887, Mitchell commissioned the elegant art nouveau church of St George's Jesmond from Thomas Ralph Spence (1848-1918), the secretary of the Newcastle Arts Association. The building is high and dramatic inside and of excellent workmanship throughout (commented upon by Bernard Shaw on his visit in the 1890s). The stained glass is especially fine, and the mosaic figures were designed by Mitchell's own son, C.W. Mitchell. The splendid Lewis organ was originally provided with air by two powerful hydraulic engines supplied by Mitchell's neighbour in Jesmond Dene, Lord Armstrong (q.v.). On the question of cost, Mitchell remarked: 'It is not what it costs, but what is best. I have built a great many ships and have made it a rule to put in the best material from end to end of them. I am building one house for God and I shall put the best material into it from east to west.'
Charles Mitchell died in 1895 and is buried in Benton churchyard, under a small obelisk of Aberdeen granite. The firm became Armstrong Whitworth in 1897. His son, Charles William Mitchell (1855-1903) was an artist and collector who had commissioned Thomas Spence to add a picture gallery to Jesmond Towers. This was completed in 1885, and the collection fittingly housed. The great painter Francis Bacon (q.v.) used to visit Jesmond Towers as a child, and remembered the coved gallery.