Dixon was born in Coalisland, County Tyrone in 1806 and entered Maynooth College at the age of sixteen.
As Primate of Armagh he held an important synod in 1854, at which all the bishops of the northern province assisted with their theologians.
The primate was a defender of the Holy See and at a public meeting in Drogheda denounced Napoleon III for complicity in the acts of the Italian revolutionists.
His speech and subsequent letter to the Freeman's Journal created a sensation and the emperor made them a subject of complaint to Pope Pius IX.
Dixon's professorship was signalized by his "Introduction to the Sacred Scriptures", a work praised by Cardinal Wiseman.