[2] Born in Tandil, Buenos Aires Province, Argentina, Saveljich joined Racing Club's youth setup in 2006, aged 15.

On 24 January 2016, Saveljich moved abroad, signing a six-month loan deal with Segunda División side UD Almería.

[6] On 4 August 2017, after contributing sporadically to the Valencian club's promotion to La Liga, Saveljich was loaned to Albacete Balompié in the second level, for one year.

[8] On 26 July 2019, Saveljich agreed to a permanent four-year deal with Rayo Vallecano, freshly relegated to the second division.

Under Ljubiša Tumbaković, the new head coach of Montenegro national team, he played in a friendly match against Greece.