Drapšin was born to a family of poor peasant farmers in the village of Turija near Srbobran (Szenttamás), Austria-Hungary a few months into World War I.

By the time he reached school age, the war ended, resulting in the Austro-Hungarian defeat and disintegration along with formation of a new state Kingdom of Serbs, Croats and Slovenes.

After completing his trade term, he enrolled in the streamlined technical high school where he first got introduced to the workers' movement ideas under the auspices of the Communist Party (KPJ), a political organization banned in the Kingdom of Yugoslavia.

In 1941, following the Axis invasion of Yugoslavia, Drapšin was given the task of organizing armed uprising in the Herzegovina region by the Yugoslav Communist Party (KPJ).

Units under his command halted German offensive in Dalmatian hinterland in January 1945 and liberated Herzegovina during the Mostar Operation.

Soon after that the 8th Corps got transformed into the 4th Army, which began the Lika-Primorje operation, an offensive against the remaining Axis forces in Yugoslavia in late March 1945.

The author and former Partisan Sava Skoko described Drapšin as a "psychologically unstable person whose condition bordered on complete insanity".