Kovačević was born in the village of Nudo near Grahovo to father Blagoje and mother Jovana (née Perović), into a family of peasants.

In his early age he worked as a lumberjack and blacksmith and adopted communism, becoming a member of the Communist Party of Yugoslavia (KPJ) in 1925.

In February and March 1943, during the Battle of Neretva, (German operation Weiss) Kovačević commanded his brigade in attacks on Prozor against the Italians and Konjic against joint Italian-Ustasha-German defenders.

On 6 June during the Battle of Sutjeska (German operation Schwarz) he became the commander of the 3rd Shock Division of the Yugoslav People's Liberation Army.

On 13 June, Kovačević was killed while personally leading his men during a charge against trenches held by the German 118th Jäger Division at Krekovi near Tjentište, Eastern Herzegovina, on the Sutjeska river.

[3] Sava Kovačević died on June 13, 1943, during the Battle of Sutjeska, while leading a charge against German positions held by the 118th Jäger Division at Krekovi near Tjentište.