In addition to his family, young Vinko's spiritual formation was deeply influenced by the Trappist Mariastern Abbey, located not far from his native village.

Puljić was ordained to the priesthood by Bishop Stjepan Bauerlein on 29 June 1970, and then served as a chaplain in the Diocese of Banja Luka until 1973, whence he became an official of the diocesan curia.

He received his episcopal consecration on 6 January 1991 from John Paul II himself, with archbishops Giovanni Battista Re and Justin Francis Rigali serving as co-consecrators, at St. Peter's Basilica.

[2] When the Bosnian War broke out in 1992, Puljić immediately became involved in helping the thousands of refugees and exiles, mobilizing all the forces of the local Church.

John Paul II once said to him, "When I imposed hands on you...to consecrate you in the office of Pastor of the Church of Sarajevo, I had no idea that very shortly your cross would be so heavy and your cup so bitter."

Puljić, speaking at the 2004 assembly of the Synod of Bishops, said that the unity of the Church is threatened by the disobedience of the Franciscan monks serving at Međugorje, who "impose their own points of view".

He confirmed that he will continue to try to establish a dialogue and peaceful coexistence between Christians and Muslims in Bosnia and Herzegovina, which was disrupted by the recent war in the country.

[6] In May 2016, Puljić drew controversy [7] after appealing to women in a sermon in Zadar, Croatia not to have sexual intercourse before marriage so that they wouldn't become a "štraca", which is a local slang word for a "whore".