Slavka Atanasijević studied music privately in Osijek: voice with Ivan Nepomuk Hummel (1820–1896), violin with director of the Croatian Vocal Society "Linden" ("Lipa") Theodor Machulka (1848–1920), and piano with Đuro Trischler.
Atanasijević gave concerts in Sombor, Osijek (with the „Linden” Vocal Society), Novi Sad, Subotica, Zagreb, Pest, Graz, and Vienna.
Following her unfortunate marriage to the Polish painter Andrzej Eugeniusz Kwiatkowski, who was on duty as a land surveyor in cadastre registry in Bosnia, she withdrew from the public spotlight in 1882, and died in Vienna, aged 47.
As a composer and pianist, Slavka Atanasijević received recognition from pedagogues, artists, and critics of her time (e.g., Franjo Kuhač and Antun Schwartz).
Influences of virtuoso, salon-style of Alexander Dreyschock and Franz Liszt in Atanasijević's works were noted in articles by music critics and historiographers.