Mat started to ride dirt bikes at the tender age of four, following the footsteps of his grandfather and father, who were both motocross riders. Like most of his fellow riders, he spent most of his youth racing and embarked on a professional motocross career before switching over the FMX. His competitive FMX career took off in 2005 when he won multiple titles on the IFMXF series. But that wasn't enough for the young man from Payerne. Mat decided to move to California for a part of the year to take the opportunity of training in more favorable weather conditions, because the weather is often dominated by rain and snow during parts of the year at home, in his native Switzerland. The move paid off and his international career got a boost. In January 2006, he won his first silver medal at the Winter X-Games. In March of that same year, he won the Red Bull X-Fighters event in Mexico City, beating his idol Travis Pastrana (USA). "This is the best day of my life!" said Rebeaud after his victory.
After recovering from a broken femur, Rebeaud was back on track stronger than ever in 2007. With only two weeks of training on a motorcycle, he just missed the podium at the Red Bull X-Fighters 2007 stop in Mexico City. Shortly afterwards, he won the Night of the Jumps on his home turf in Basel, Switzerland, and he came in second behind Travis Pastrana at the Red Bull X-Fighters tour stops in Slane Castle, Ireland, and Madrid.
Rebeaud was the dominant force in 2008; so far the best of his career, winning the first stop of the series in Mexico City and then got second in Rio de Janeiro, Brazil. He also claimed his first victory on U.S. soil at the Red Bull X Fighters in Fort Worth, Texas, then he went on to win the prestigious event in Madrid. He also claimed an X-Games Silver Medal in Moto X Freestyle and won his fourth Red Bull X-Fighters event of that year in Germany to become the tour champion even before the final event in Poland.
Even though he was unable to get back to top form after a series of injuries in 2009, Rebeaud still had a chance to win the Red Bull X-Fighters World Tour at the season finale in London. Unfortunately, he missed out on back-to-back titles as Nate "The Destroyer" Adams powered to victory. The year 2010 started with an almost fatal crash while practicing ahead of the first event in Mexico. Rebeaud was glad to be back on his bike in the summer to ride the event in Moscow, as his first contest in the year. His 10th place showed that he was not really back into top shape, but it was a good opportunity to gain new confidence for the event in Madrid, where he grabbed a strong second place. Finishing sixth in London and ending up fifth in Rome helped him to get a seventh place overall in the final tour ranking, a remarkable achievement considering he missed the first third of the season.
In March 2011, while practicing the Volt (Body Varial), Mat broke his left femur and was sidelined for almost the entire season. His comeback for Red Bull X-Fighters in Dubai did not work out as planed, as the pain in the injured leg was still too great to perform. He was back for a part of 2012, taking ninth in Madrid and 10th in Dubai. His 10th place in Munich left the impression that Rebeaud was riding in pain.
The last two years have been difficult for the high flyer from Switzerland and he was definitely down, but he was not out as recent film footage from his training and a few shows proved. In 2013, the KTM rider was able to win a few events and grab a silver and a bronze medal at X-Games. He got unlucky at his two Red Bull X-Fighters appearances with results that did not satisfy him and this leaves room for more in 2014. Rebeaud proofed already in 2005 that he can come back stronger from tough times.