Born on July 15, 1932, to Granville H. and Harriet (Shepherd) Beever, he was raised in Sharon, Massachusetts, attended local schools, and then graduated from Williston Academy. At the University of New Hampshire as an engineering student, he first met his future wife, Sarah Jane Andrew. Mike left school to serve his country in the U.S. Army during the Korean War. Upon returning to the States he married Jane in 1956 and finished his degree in Civil Engineering at UNH.
He was employed after graduation at U.S. Steel in Pittsburgh, but then with a growing family moved to Gorham, Maine, in 1961. He worked for a short time at L.C. Andrew Lumber Company, and then bought the C.E. Carll Insurance Agency, which had been named for Jane’s grandfather. The insurance office grew and was successful under his direction for over 30 years. In 1992 his son Jason Beever joined the company and took over leadership as the fourth generation in the family business when Mike retired in 1994.