It was produced by Sam Petts-Davies and recorded in Oxfordshire and Abbey Road Studios, London, in the same sessions as the previous Smile album, Wall of Eyes (2024).

The Smile promoted Cutouts with the singles "Don't Get Me Started", "The Slip", "Foreign Spies", "Zero Sum" and "Bodies Laughing", music videos by the digital artist Weirdcore, and a series of cryptic messages on social media.

"[9] He connected this to the "atomisation and isolation from world events" caused by social media, and asked: "Why the fuck would we be online with two-dimensional avatars of each other as if they are really us, and try to engage with complex issues using two or three sentences?

[20] "Instant Psalm" features strings, an "earthy" melody and an acoustic guitar playing a pedal note, which Loud and Quiet likened to Radiohead's 1995 album The Bends.

[16] In March 2024, the Smile began a European tour, including a performance at 6 Music Festival in Manchester with the London Contemporary Orchestra.

[24] "Don't Get Me Started" was added to digital services on 8 August, accompanied by a video directed by the audiovisual artist Weirdcore, with "glitchy" computer graphics reminiscent of generative artificial intelligence.

[8] On October 1, the Smile announced a pair of art installations, Through the Glass, in London and New York City, with new songs and Weirdcore visuals.

[37] The Slant critic Lewie Parkinson-Jones said Cutouts struck a good balance of styles and better resembled "the work of a proper band" than Yorke's previous side project, Atoms for Peace.

[15] In The Arts Desk, Graham Fuller wrote that Cutouts was "not without beauty and technical brilliance", praising Yorke's "intimate" singing and Greenwood's "dextrous" guitar work.

[40] The Loud and Quiet critic Sam Walton said that while Cutouts was less cohesive, its songs were "uniformly enthralling, captivating, thrilling and memorable", and suggested it was Yorke and Greenwood's best work since the 2007 Radiohead album In Rainbows.

[41] Pitchfork described it as a "a thrilling testament to the near-telepathic chemistry these three musicians have honed across two years of touring", and felt the tracks where Skinner is least present, "Foreign Spies" and "Don't Get Me Started", were the only weak points.