Arbuthnot was born in Liverpool, England, the son of George Clerk Arbuthnot (1803–1876) of Marisbank, Midlothian, (the third son of Sir William Arbuthnot, 1st Baronet), by his second wife Caroline Ramsay, daughter of James Hay of Collepriest, and Lady Mary Ramsay, the fourth daughter of George Ramsay, 6th Earl of Dalhousie.
Arbuthnot entered the Royal Navy as a cadet in September 1863, aged 13, and was commissioned as a sub-lieutenant in December 1869. He was promoted to the rank of lieutenant from the Royal Yacht Victoria and Albert II on 7 September 1871. In 1875-1876 he served aboard the yacht Pandora in the Arctic, earning the Arctic Meda
Arbuthnot was promoted to the rank of commander on 31 December 1883, and to captain on 30 June 1891.
In 1888 he was stationed in Zanzibar where he served in the Royal Navy"s Anti-Slavery Squadron. He commanded the cruisers Orlando during her operations on the Australia Station between 1892 and 1895, and Crescent from January to March 1895.
From January 1896 until April 1898 he was in command of the protected cruiser Hermione, which formed part of the Flying Squadron of 1896, and then the battleship Resolution between April 1898 and March 1900. From August 1900 until August 1903, he was in command of the HMS Cambridge, gunnery ship off Plymouth.
He was appointed a Naval Aide-de-Camp to King Edward VII on 9 September 1901, serving until promoted to the rank of rear-admiral on 1 January 1904.
In accordance with the provisions of the Order in Council of 8 December 1903, Arbuthnot was placed on the Retired List on 1 July 1907. He was promoted to vice-admiral on the Retired List on 22 March 1908, and to admiral on 18 September 1911. He died on 30 September 1913.
