Mattheis started cycling with RSC Kempten. As part of Team Auto Eder Bayern, he won the 2013 German Cycling League in the junior category, came third in the German Championships in the individual time trial, and 25th in the road race at the World Championships.
In his first year as a senior in 2014, Mattheis rode for the UCI Continental Team Heizomat and, at the beginning of 2015, for the MLP Team Bergstraße. After not being active at the international level, he finished tenth overall in the 2022 Tour de Guadeloupe as a guest rider for the Embrace the World Cycling team.
He joined the Continental Team Bike Aid for the 2023 season. He was successful for this team in Turkish stage races in 2024, finishing second overall in the Tour of Mersin and winning the third stage of the Tour of Routhe Salvation. In 2025, he won the prologue of the Tour of Istanbul, his first UCI category 1 race. In September 2025, he won the opening stage of the Chinese Tour of Poyang Lake, which he finished second overall. He was then nominated by German Cycling for the European Championships.