The graduate of the Schladming Ski School celebrated his first major success on March 10, 1999 at the Junior World Championships in France when he won the bronze medal in the downhill. In 2000 and 2001 he won the Junior World Championships in his special downhill discipline. On March 15, 2000 he contested his first World Cup race in the downhill at the World Cup final in Bormio, which he finished in 24th. Graggaber achieved his best placement in the World Cup in his only second World Cup race on November 30, 2002 in Lake Louise with eleventh place. He could not confirm this performance in the next few years. By the end of 2004 he had only reached points once in twelve World Cup runs. His results in the European Cup were better : by January 2005 he had won five downhill runs and a Super-G. In the 2003/04 season he was first in the downhill classification and second in the overall European Cup classification.
On January 15, 2005, Graggaber achieved another good result in the World Cup with 15th place in the Lauberhorn run in Wengen . In the next week he had a bad fall while training for the Hahnenkamm run on the Streif in Kitzbühel , suffered a serial fracture of the rib and injuries to the lungs as well as a fracture of the head of the humerus in the left shoulder. He had to take a break for almost a year. After that, Graggaber mainly played in the European Cup and less often in the World Cup. In the World Cup he achieved two top 30 results after the injury break; in the European Cup he achieved numerous top 10 results and fifth place in the downhill classification in the 2007/08 season . After the 2008/09 season, Graggaber ended his career.