Beghe was born in Illinois, the son of Emmavve (née Frymire) and Bruno Beghe, an Italian-born painter, sculptor, and violinist. Beghe received his bachelor's degree from the University of Chicago in 1951 and his J.D. from the University of Chicago in 1954. While a student, he joined Phi Beta Kappa, Order of the Coif and Phi Gamma Delta. Beghe is co-managing editor of Law Review, He was admitted to New York Bar in 1955 and practiced law with the New York City firm of Carter Ledyard & Milburn until 1983. He practiced with New York City firm of Morgan, Lewis & Bockius until 1989. President George H.W. Bush appointed him as a Judge in United States Tax Court on March 26, 1991, for a term ending March 25, 2006. Beghe retired on February 28, 2003, but continued to perform judicial duties as a senior judge on recall. Beghe died on July 7, 2012, after a long illness.
Beghe was a member of numerous professional organizations, including the American Bar Association, Tax Section; the International Bar Association; Business Section Committee N (Taxation); Judge's Forum; Human Rights Institute; International Fiscal Association; American Law Institute, American College of Tax Counsel; and the Honorable Order of Kentucky Colonels.