David Schütter was born in 1990 in Hamburg. He completed an acting course at the Schule für Schauspiel in Hamburg from 2009 to 2013. During these years, he already got minor roles in various television programmes. He gave his debut on the big screen in Gregor Schnitzler's "Spieltrieb" ("Gaming Instinct", 2013). In this drama, Schütter portrays the best friend of Jannik Schürmann's leading character. Afterwards, Schütter played guest roles in German television series, including "Der Lehrer" (Episode: "Wieder so ein fieser Vollmer-Trick", 2014) and in "Marie Brand und das Mädchen im Ring" (2014). In two episodes of "Tatort" ("Kopfgeld", 2014 / "Der große Schmerz", 2016), Schütter played the boyfriend of Lenny (Luna Schweiger), the daughter of inspector Tschiller (Til Schweiger). He further portrayed an aspiring detective in six episodes of the crime series "Josephine Klick – Allein unter Cops" (2014).

Schütter got his first leading role in a film in the award-winning "Porn Punk Poetry" (2014) in which he played a male prostitute who falls in love with a young Russian woman. He also had an important role in the highly anticipated drama "Wir sind jung. Wir sind stark." ("We Are Young. We Are Strong.") which premiered at the Rome Film Festival and was released in German cinemas in 2015. The film is based on a true story of a group of neo-Nazis who attacked a shelter for asylum-seekers in Rostock in 1992.

In the acclaimed television series "Weinberg" (2015), Schütter played a gifted football player, who hides his homosexuality and has an affair with a catholic shop owner. Additionally, he played a modern hermit as a part of the ensemble in the fantasy film "Offline - Das Leben ist kein Bonuslevel" ("Offline - Are You Ready for the Next Level?", 2016). Schütter was also seen as Demetrius in "Shakespeares letzte Runde" (TV, Director: Achim Bornhak). In "Das kalte Herz" ("Heart of Stone"), he played the greedy rival of Peter Munk.

Schütter had a leading role in "Unsere Zeit ist jetzt" (2016), in which he played one of three young filmmakers who want to make a film about the Hip Hop Star Cro. For his role in "Strawberry Bubblegums," Schütter received the 2017 Studio Hamburg Young Talent Award.  

David Schütter then appeared in front of the camera for Florian Henckel von Donnersmarck's "Werk ohne Autor" ("Never Look Away"), which was released in 2018 and nominated for a Golden Globe and an Oscar. In the same year, he played the manager of a club in St. Pauli in Jakob Lass' Hamburg neighborhood comedy "So was von da" ("Right Here, Right Now"). In the acclaimed gangster series "4 Blocks" (2018), he played a central role as a Berlin real estate shark, and in the two-part TV thriller "Walpurgisnacht" (2019), he was an amateur photographer who comes under suspicion of murder as a possible misogynist. The multi-part "Unsere wunderbaren Jahre" ("Our Wonderful Years", 2020), set in the postwar era, featured Schütter as a communist factory worker. He received a nomination for the Hessian Television Award for this role.  

On the big screen, David Schütter was seen as a police officer in the adventure comedy "Sweethearts" (2019), in the ensemble of the action film "Charlie's Angels" (US/DE 2019) and as an SS man in the concentration camp drama "Persischstunden" ("Persian Lessons", RU/DE/BR 2020). In the Netflix series "Barbarians," which launched in late 2020, Schütter starred as a Cheruscan warrior; the six-part series "Westwall" (2021), about a police student who becomes involved in the machinations of a far-right network in the police force, he embodied one of the right-wing extremists. Schütter also appeared on camera in 2021 for the feature film "In einem Land, das es nicht mehr gibt" ("In a Land That No Longer Exists"), in which he played a rebellious GDR fashion photographer. It was released in the fall of 2022.