Born in Hamburg, a city in Northern Germany, David Schütter is grandson of the German actor Friedrich Schütter. He studied acting in Schule für Schauspiel Hamburg [de] between 2009 and 2012. Before the school, he had already made his screen debut in the NDR series Die Pfefferkörner in 2008, following another appearance in Da kommt Kalle, in 2010. In 2011, he had a supporting role in the ZDF crime detective series Stubbe – Von Fall zu Fall, and another supporting role in Küstenwache in 2012.
Shortly after graduation, Schütter made his film debut in Gaming Instinct [de], in 2013. From 2013 to 2014 he portrayed more than 13 roles in various series, among which are Alles Klara [de], Marie Brand [de], Cologne P.D., In aller Freundschaft, Tatort, Großstadtrevier and Der Lehrer. In the last one, together with Hendrik Duryn [de], he played the role of a problem student named Florian Klosterkämper. He was cast in the title role of the 2014 documentary miniseries Alexander the Great, whom he played 'in a dramatic exaggeration, spitting out the big notes instead of articulating them'. He also played the lead role in the 41-minute short film Porn Punk Poetry (2014). With tattoos, bleached hair and mohawk, he embodied the 27-year-old Damon, who works as a male prostitute, but is now too old for this gay scene and is at a turning point in his life when he meets the young Russian Emma. Schütter represented 'a soul between hardship and romance'. The same year he starred in the award-winning drama film We Are Young. We Are Strong, as neo-Nazi Sandro.
Following some guest and supporting roles in Letzte Spur Berlin [de] (2015), Alarm für Cobra 11 – Die Autobahnpolizei (2015), Weinberg (2015), Offline: Are You Ready for the Next Level? [de] (2016), Der Kriminalist (2017), Rübezahls Schatz [de] (2017) and Right Here Right Now [de] (2018), Schütter starred in the second season of 4 Blocks as Matthias Keil, one of the leading roles. In the 2019 two-part television thriller Walpurgisnacht – Die Mädchen und der Tod, he embodied the amateur photographer Alexander Zimmermann, who is suspected of being a possible misogynist.

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