Ignatius Mrak was born on October 16, 1810, in Hotovlja, in the Duchy of Carniola of the Austrian Empire (present-day Slovenia), as one of six children of Mathias and Maria (née Demscher) Mrak, and baptized Ignatz Mrack.

He received his early education in Poljane and Kranj, then attended the Bežigrad Gymnasium in Ljubljana, entering the diocesan seminary there in 1834 and completing theological studies with honors.

Ordained a priest for the Diocese of Ljubljana on August 13, 1837, by Prince-Bishop Anton Aloys Wolf, he served briefly as a tutor to the son of Baron Peter Pirquet in Legnago before returning to Carniola as an assistant pastor in Poljane and Slavina.

Inspired by fellow Slovene missionary Frederic Baraga's work with Native Americans in the Diocese of Detroit, he sought incardination there and arrived in Michigan in late 1845, quickly mastering the Ottawa dialect to preach his first sermon in it just one month later.

Assigned initially to assist Francis Pierz at L'Arbre Croche missions in the Upper Peninsula, he later led St. Anthony's in Cross Village and missions at St. Francis Xavier's in Readmond, St. Leopold's on Beaver Island, and Immaculate Conception in Peshawbestown.

In 1853, Pope Leo IX established the Vicariate Apostolic of Upper Michigan with Baraga as vicar apostolic, into which Mrak was incardinated; it became the Diocese of Sault Sainte Marie in 1857, with Baraga as bishop appointing Mrak vicar general in 1859 despite his pleas to return to Slovenia.

On September 25, 1868, Pope Pius IX appointed Ignatius Mrak to succeed the late Baraga as Bishop of Sault Saint Marie and Marquette, though he reluctantly accepted after months of delay and was consecrated on February 7, 1869, by Archbishop John Purcell at St. Peter in Chains Cathedral in Cincinnati, with Bishops Peter Lefevere and John Henni as co-consecrators.

During his tenure, he attended the First Vatican Council (1869–1870), modestly expanded the diocese by adding six churches and five priests amid economic depression in the Copper Country, ordained future bishops John Stariha and Frederick Eis, but faced challenges like school closures and placing a Hancock church under interdict in 1874.

Afflicted by rheumatism, Ignatius Mrak resigned on April 28, 1879, with Pope Leo XIII accepting and granting him the titular see of Antinoë; he then pastored in Negaunee and Menominee, resumed missionary work in Peshawbestown, and from 1891 served as chaplain at St. Mary's Hospital in Marquette.

He died there on January 2, 1901, at age 90, and was buried in the crypt of St. Peter's Cathedral.