He was born on 16 November 1921 in Humenné. He was a painter, sculptor, monumentalist, illustrator, restorer, iconographer and philosopher. He ranks among the most significant representatives of Slovak visual art. He studied at the Vocational Woodworking School in Humenné, where his talent was noticed by his drawing teacher — academic painter Jozef Chovan. From 1943 to 1945 he studied at the Slovak University of Technology in Bratislava, in the drawing and painting department under Ján Mudroch. In 1948 he graduated from the School of Applied Arts in Prague under Professors František Tichý and Jozef Novák. From 1950 he lived and worked in Bratislava. In terms of expression, he drew primarily from traditional Byzantine iconography. In his work he emphasised the beginnings of Slovak national history and the period of Great Moravia, creating icons of several personalities from that era. He was also inspired by ancient Slavic history, the history of Christianity, immortality, motherhood, family and society.

Through his extensive body of work, he made an impact on almost every area of visual art. Klimčák’s tapestries and paintings adorn the spaces of the highest institutions of the Slovak Republic. The six-metre-long tapestry Byzantine Mission in Great Moravia, woven over nearly three years, graces the historic walls of Bratislava Castle. The immortal mythical bird Phoenix, rendered by the master in art-protis, hangs in the National Council of the Slovak Republic — his gift to parliament on the occasion of the establishment of the independent Slovak Republic on 1 January 1993. Several of his works also adorn the Constitutional Court in Košice. The tapestry Patrons of Europe — Saints Cyril and Methodius is in St. Martin’s Cathedral in Bratislava. Also worth mentioning are the stained-glass window in the hospital in Revúca (1957), the tapestries Jánošík (1960), Slovakia (1973), New Life (1972), Work (1972), a mosaic design for Prague Castle in tempera (1965), and mural paintings at a primary school in Bratislava, at the Tatranská Lomnica recreational centre and at the Piešťany spa.

He contributed to the decoration of many Greek Catholic churches in Slovakia through the creation of icons, frescoes, crosses and more. The sarcophagus of the Greek Catholic martyr bishop Peter Pavel Gojdič (1888–1960) in the Cathedral of St. John the Baptist in Prešov was also realised according to his design.

He participated in numerous nationwide exhibitions and competitions.

He worked and created across a wide range of monumental techniques, including woven tapestry, art-protis, textile collage-appliqué, stained glass, stucco lustre, mosaic, concrete relief and wooden objects. He is regarded as a master of stained glass in both sacred and secular architecture. He was also a member of the stamp commission and is the author of several notable postage stamps — for example, his Christmas stamps rank among the finest Slovak stamps with a Christmas motif. On the occasion of his 100th birthday, the Slovak Post issued a stamp featuring a portrait of Mikuláš Klimčák in December 2021.

In 1999 he self-published the richly illustrated representative work Proglas of Constantine the Philosopher — the poetic Preface to the Old Church Slavonic translation of the Gospel, in a Slovak translation by poet Viliam Turčány — which many foreign heads of state took home from Slovakia as a gift from the President of the Slovak Republic.

In his work he wished to bear witness to contemporary life, to the great historical past of the nation, to the poetry of modern living, and above all to the historical legitimacy of his people’s right to an independent national and social life.

He died on 2 March 2016 in Bratislava and is buried at the Ondrejský Cemetery.

For his work, M. Klimčák received many awards, including the Fra Angelico Prize (2003) awarded by the Council for Science, Education and Culture of the Conference of Bishops of Slovakia; in 2007, Pope Benedict XVI appointed him Knight of the Order of St. Sylvester — the highest ecclesiastical honour for laypeople in the Catholic Church; and the Gold Medal of Matica slovenská (2011). In 2011, the President of the Slovak Republic Ivan Gašparovič awarded him the state honour — the Medal of the President of the Slovak Republic.

In Prievidza, two sgrafitos by M. Klimčák can be found on Fraňa Madvu Street: Man with a Woman and a Flute and Family (Behind the Spruce).