Mawson made his motorsport debut at the age of seven . Like most other automobile racing drivers, he was in kart racing in various championships in his early days , of which he won the Australian Junior Championship in 2010. Finally he took part in the 2013 Kart World and European Championships. Mawson drove his first season in a monoposto in 2014 in the French F4 championship. He succeeded, his first race in Formula racing in Le Mans win. He finished the season fourth in the championship.
In 2015 Mawson moved to the Dutch racing team Van Amersfoort Racing in the newly founded German Formula 4 championship . He became a teammate of Harrison Newey and Mick Schumacher . Mawson drove the first racing weekend with a German racing license and denied the rest of the season for Australia. Mawson won five races and finished the season as the best driver of his team in third. In 2016 Mawson stayed with Van Amersfoort in the German Formula 4 championship. He starts this year with a German racing license. At the end of the season Mawson was champion with 52 points ahead of Mick Schumacher.
In 2016/17 Mawson competed in the MRF Challenge Formula 2000 . At the end of the season he finished second with three wins and nine other podium finishes behind Harrison Newey , who was tied for points and scored seven victories of the season. Mawson lost the title he had previously believed to be safe due to a driving error in the last race, which pushed him back from first to third place four laps before the end of the race. In 2017 Mawson switched to the European Formula 3 championship , in which he continued to compete for Van Amersfoort Racing.