Amundson was born in Pendleton, Oregon but grew up in Aberdeen, South Dakota. At Aberdeen Central he excelled in football, basketball, baseball, and track & field. As a high schooler Amundson set the state record in shot put and discus, the latter of which he still holds. In football he was selected to the all-state team both as a linebacker and quarterback.
Amundson was recruited to Iowa State both as a track & field athlete and as a football player. He would ultimately become a seven time letter winner, four in track & field and three in football.
The football field is where Amundson truly excelled and gained most of his recognition. George was recruited as a quarterback but had to play tailback his junior season due to several injuries on the team. He led the Cyclones to their first ever bowl berth in the 1971 Sun Bowl. That season he rushed for a then-record 1,260 yards and 15 touchdowns. His senior season he was able to switch back to his natural position of quarter back where he became the first Cyclone to top 2,000 yards of total offense in a season. His 2,387 yards set a Big Eight Conference mark and earned him Big Eight Player of the Year honors, beating out Nebraska'sHeisman Trophy winner Johnny Rodgers.
At the conclusion of his collegiate career, Amundson was drafted by the Houston Oilers with the 14th overall pick in the 1973 NFL Draft. He is the first and only first round NFL draft pick in Iowa State history. Amundson would play the following two season with the Oilers and his final NFL season with the Philadelphia Eagles. His career stats are 74 rushes for 194 yards and four touchdowns, three of them coming in one game.