Apollon Dashkov participated in the Russo-Turkish War, 1768-1774: in 1771 Dashkov took part in the march from the Taganrog fortress to Crimean peninsula to the Yenikale Strait fortress, which was soon taken by the Russian detachment commanded by Prince Fiodor Fiodorovich Shcherbatov [ru], later in 1772 and 1774 in marches against Crimean Tatars.
For a few times he secured positions of quartermaster, and in 1782 and 1783 Dashkov was in Crimea, and later in the army of frontier division as captain.
After the annexing of Crimea, he attended the triumphant present oath of citizenship to Russia by Tatars at the Karasu-bazar.
On October 8, 1802, tsar Alexander I of Russia appointed Apollon Dashkov as the first governor-general of Taganrog, where he was charged with reconstruction of the fortress.
During Dashkov's governorship (1802–1805) were built several fortress buildings: infirmary, officers headquarters and barracks; improved the equipment of the municipal fire-brigade.