After his return, Ōsumi was promoted to lieutenant, and served as chief navigator on the cruisers Saien and Matsushima, and the patrol ship Manshu during the Russo-Japanese War.

After serving in a number of staff positions, Ōsumi was assigned as naval attaché to Germany from 27 January 1909 to 1 December 1911.

He spent a year as executive officer on the battlecruiser Tsukuba from 1913 to 1914, returning to staff positions until 1 December 1917, when he received his first command: the battleship Asahi.

Although the commander of the Combined Fleet, Admiral Sankichi Takahashi ordered his battleships in Tokyo Bay and targeted the rebel positions, and the commander of the Yokosuka Naval District, Admiral Shigeyoshi Inoue organized a land force to march on Tokyo, Ōsumi refused to issue any orders or take any action, despite word that Prime Minister Okada Keisuke had survived the attack.

In 1940, on the retirement of Prince Fushimi Hiroyasu, Ōsumi became the most senior admiral in the Imperial Japanese Navy; however, he was bypassed for promotion by Osami Nagano.

Ōsumi was killed in action in the Second Sino-Japanese War during an inspection tour of the front lines on 5 February 1941, when his plane, an Imperial Japanese Airways transport, was shot down by Chinese guerrillas soon after takeoff from Guangzhou on a flight towards Japanese-occupied Hainan.