Acheampong was born on 23 September 1931 to Catholic parents of Ashanti origin. He attended Roman Catholic schools in Trabuom and Kumasi, and later studied at the Central College of Commerce in Agona Swedru.

Before joining the military, Acheampong worked as a stenographer at Timber Sawmill in Kumasi, taught at Kumasi Commercial College, and eventually became Vice Principal at Agona-Swedru College of Commerce.

During his tenure, Acheampong introduced significant initiatives such as "Operation Feed Yourself" (promoting self-reliance in agriculture), "Operation Keep Right" (switching traffic from left-hand to right-hand driving), and national reconstruction projects aimed at employment and urban development.

Acheampong trained as a cadet officer at Aldershot, England, and was commissioned into the Ghana Army in 1959. He participated as a UN peacekeeper during the Congo Crisis.

In response to political pressures, Acheampong proposed a controversial 'Union Government' that would share power between civilians and the military. This led to student protests, university closures, and violent clashes.

Following a military uprising led by Jerry John Rawlings on 4 June 1979, Acheampong was court-martialed and executed by firing squad on 16 June 1979 along with General Edward Kwaku Utuka.

Acheampong was married to Faustina Acheampong. His granchildren include American football player Charlie Peprah and Fulham F.C. striker Yakini Acheampong. Kutu Acheampong was raised in a Christian home, in the catholic denomination.