Mitchell was commissioned in January 1782 with the rank of ensign, in the service of the 101st Regiment of Foot. After promotion to lieutenant in June 1783 and served in Canada from 1786 to 1796. He fought in the Egyptian Campaign in 1801 and was promoted to lieutenant-colonel in December 1805 in the service of the 26th Regiment of Foot.
He became a major on 17 March 1804 and lieutenant-colonel on 12 December 1805.
Mitchell commanded a battalion of the 26th Regiment of Foot from 1805 to 1811 and the 51st Regiment of Foot from 13 June 1811 until 1814, throughout the Peninsular War. He gained the rank of colonel on 4 June 1813.
In the Waterloo campaign Mitchell commanded the 4th Brigade of the 4th Division, consisting of the 3rd battalion of the 14th foot, the 1st Battalion of 23rd Fusiliers, and the 1st Battalion of the 51st Light Infantry, a total of around 2,000 officers and mentor "As the light was beginning to fail (on 17 June 1815) Colonel Mitchell led his brigade to the position.. on the extreme right near Braine-l"Alleud, and here the regiments bivouaced for the night, the rain continuing to fall in torrents." Mitchell"s brigade was engaged early in the battle when the French attacked Hougoumont Farm."
He was conferred with the honour of Companion of the Order of the Bath on 4 June 1815 and received the Russian Order of Saint Vladimir.
He died on 20 April 1817 at age 46 at Queen Anne Street, London, England.
Mitchell married Lady Harriet Isabella Somerset, daughter of Henry Somerset, 5th Duke of Beaufort and Elizabeth Boscawen, on 3 July 1804. The children of Colonel Hugh Henry Mitchell and Lady Harriet Isabella Somerset were:
Margaret Harriet Isabella Mitchell (4 June 1806 – 29 June 1876), who married, on 15 January 1833, the Review Thomas Walpole, Canon of Winchester Cathedral, elder brother of Home Secretary Spencer Horatio Walpole, and had issue.
Charlotte Gertrude Elizabeth Mitchell (6 December 1807 – 4 August 1876), who married, on 18 April 1825, John Leveson-Gower and had issue.
Colonel Hugh Andrew Robert Mitchell (12 September 1816 – 21 August 1857), of the Grenadier Guards, who married, on 30 July 1844, Sarah Lowndes and had issue.