He briefly interrupted his academic education to serve in the Yugoslav People's Army in Subotica in 1977 and Zrenjanin in 1978.

[1] Vukšić served as a chaplain at the Mostar cathedral and worked as a journalist for the diocesan magazine Crkva na kamenu from 1980 to 1982.

[1] On 1 February 2011, Pope Benedict XVI appointed him the first bishop of the Military Ordinariate of Bosnia and Herzegovina.

[citation needed] On 22 January 2020, Vukšić was appointed archbishop coadjutor of the Metropolitan Archdiocese of Vrhbosna[4] and two days later he was named Apostolic Administrator of the Military Ordinariate of Bosnia and Herzegovina.

[1] He succeeded as Metropolitan Archbishop of Vrhbosna upon the resignation of his predecessor Cardinal Vinko Puljić on 29 January 2022.