Mung'andu was born in Kasisi around 1923 and went to primary school there. He went to secondary school in Chikuni where he also studied to be a teacher. In 1943, he went to the seminary at Chishawasha in Zimbabwe  being ordained as a priest in 1950.
During the 1950s and early 1960s, Mung'andu worked as a parish priest and as a principal of the Kasisi Boys School. He was made Vicar-General of Lusaka in 1963 before being moved to a parish in Livingstone in 1969. Pope Paul VI appointed him as Bishop of Livingstone in 1975 before Pope John Paul II promoted him in 1984.