Mies began his racing career in 2006 in the Toyota Yaris Cup Germany and contested the Ford Fiesta Cup Germany in 2007. In 2008 he won Division 2 of the ADAC Procar Series in a Ford Fiesta ST, while also making his first GT racing appearances in the ADAC GT Masters at the wheel of an Audi R8 LMS, beginning a long association with the Audi brand.
Mies secured his first major championship title in 2009, winning the FIA GT3 European Championship for Phoenix Racing alongside Christopher Haase in an Audi R8 LMS. He moved to Abt Sportsline for the 2010 ADAC GT Masters, finishing second in the championship.
In 2011, Mies took his first Bathurst 12 Hour victory driving for Joest Racing alongside Marc Basseng and Darryl O'Young. He won the race again in 2012, this time with O'Young and Christer Jöns for Phoenix Racing, making him a back-to-back winner at Mount Panorama. He followed those results by winning the 2012 Blancpain Endurance Series.
The 24 Hours Nürburgring became a defining event in Mies' career. In 2015 he won the race for the first time alongside Nico Müller, Edward Sandström, and Laurens Vanthoor in the new Audi R8 LMS for Team WRT. In 2017 he claimed a second Nürburgring 24 Hours victory alongside Kelvin van der Linde, Connor de Phillippi, and Markus Winkelhock, this time for Land Motorsport.
Mies won the ADAC GT Masters twice. In 2016 he took the title alongside Connor De Phillippi. He returned to the top of the ADAC GT Masters standings in 2021, this time with Ricardo Feller as his partner, adding a second series title to his record.
In 2015, beyond his Nürburgring success, Mies also won the Australian GT Championship and the Australian Tourist Trophy for Jamec Pem Racing, demonstrating his versatility across multiple continents. He defended his Australian GT title in 2016 while continuing in the Blancpain GT Series, finishing second in the series.
Mies returned to GT World Challenge Europe in 2023 with Saintéloc Racing alongside Simon Gachet and Patric Niederhauser in the Endurance Cup Pro class, as well as contesting the Sprint Cup with Grégoire Demoustier. In November 2023 he announced his departure from Audi after fourteen years, signing with Ford. He made his Ford debut at the 2024 24 Hours of Daytona, finishing sixth in the GTD Pro class.
Mies' fourteen-year tenure with Audi Sport produced one of the most decorated GT3 careers in German motorsport. His Bathurst and Nürburgring doubles, combined with multiple championship titles across three continents, cement his standing as one of the premier GT3 specialists of his era. His move to Ford Performance underlines continued demand at the highest level of GT competition well into his mid-thirties.