Blattman started participating in wheelchair athletics to improve his general fitness level. At the 1988 Seoul Games, he came fifth in the first heat of the Men's 200 m 1A – event. He competed in the Stoke Mandeville Games in 1989 and 1990. In 1990, at the World Championships and Games for the Disabled in Assen, Netherlands he won a gold medal in the men's 4x100 m relay T1 event and two bronze medals in the 100 m and 200 m T1 events. He won a silver medal in the 4×100 m event and a bronze medal in the 4×400 m event at the 1992 Summer Paralympics. At the 1996 Atlanta Games, he won a gold medal in the 1500 m event, for which he received a Medal of the Order of Australia, and a silver medal in the 800 m event. In 1998, Blattman won the Men's Marathon (T51) event at the World Championships. At the 2000 Sydney Games, he won a gold medal in the men's 400 m T51 event, a silver medal in the men's 1500 m T51 event, and a bronze medal in the men's 800 m T51 event. That year, he received an Australian Sports Medal. In 2002, Blattman came in first in the T51 Quads event at the Arrive Alive Summer Down Under Wheelchair Track and Road Racing Series 10k event, with a time of 37.52. He competed at the 2010 Optus Grand Prix in Canberra in the Men &amp; Women 5,000 metres wheelchair event, but he did not finish.