He was the son of Mikhail Ivanovich Dashkov (1736–1764) and Yekaterina Romanovna Vorontsova-Dashkova. He was educated at Edinburgh University, from 1777 to 1779, with a Master of Arts. He was on Grigory Potyomkin's staff with Korsakov. He was elected Fellow of the Royal Society 8 February 1781.
- Dissertatio philosophica inauguralis, de tragoedia. Paulus Daschkovie princeps, 1779