His father was a middle-ranking official at the time, and Neverovsky grew up alongside fourteen other children.

Young Neverovsky found a patron in Count Pyotr Zavadovsky, a friend of his father's.

Zavadovsky assisted in Neverovsky's education, enabling him to learn Russian and Latin and become a mathematician.

[3] He would fight during the Russo-Turkish war, beginning after his transfer to the Malorossiya or 'Little Russian' Grenadier Regiment, where he was promoted in October of 1787.

Part of his contributions to the regiment were improving its accuracy, as he would often host firing drills, partake in them, and would personally see to it that the men maintained their muskets well.

[2] While fighting during the French invasion of Russia, after marching to the Western border 10 days after the wars' start, he was assigned to Bagration's 2nd Western Army and was commander of the 27th Infantry Division,[3] which he had helped organise in the last months of the year prior.

Dmitry Neverovsky was able to successfully delay Marshal Ney, and the battle of Smolensk would start 2 days later.

Serving under General Fabian Osten-Sacken's Corps, Neverovsky fought at the battle of Leipzig.