As the son of a farm laborer, he attended elementary school in Luckenwalde from 1933 to 1941 and completed an apprenticeship as a commercial clerk there from 1942 to 1944.
[2][4] After attending the CPSU Higher Party School "W. I. Lenin" in Moscow from 1953 to 1956, he was appointed department head in the Bezirk Potsdam SED.
[8] On behalf of Walter Ulbricht, Wittig was one of the main people responsible for the demolition of the Garnisonkirche ruins, despite opposition from a small part of the city council, including allegedly the then mayor of Potsdam, Brunhilde Hanke.
[9] In 1970, Erich Honecker proposed him along with Harry Tisch as the chairman of the Volkskammer Committee for National Defense and successor to the late Paul Fröhlich.
[5] During the GDR era, a POS in today's Berlin district of Staaken (Spandau borough), the Potsdam Polytechnic Secondary School 45, and a street in the Waldstadt II residential area were named after him.