Born in the present day Hłybokaje District in the family of a landless nobleman, Drazdovič studied in Dzisna Vitebsk Region, after that in Vilnia under Ivan Trutnev.

Jazep was born on October 13, 1888, in the village of Punki, Dzisna County, Vilna Province, in the family of an impoverished nobleman.

At this time, he made his first steps in art: he created a series of graphic works with landscapes of the Dzisna region, decorated the cover of the "First Belarusian Calendar for 1910", published by Nasha Niva.

Drazdovich met the First World War in the active army, with a reserve battalion on the Western Front.

Due to difficult working conditions, Jazep Drazdovich fell ill with typhoid fever and was hospitalized for two months.