Slant called Cutouts "more challenging" than Wall of Eyes, focusing on atmosphere over traditional songwriting. Pitchfork described it as "looser" and "funkier." The lyrics tackle themes like capitalism, climate change denial, and sociopolitical anxiety. Uproxx noted "Don't Get Me Started" for its "synth-heavy" and "propulsive" sound. "Zero Sum" is fast-paced with "hyperactive" lead guitar. "Eyes & Mouth" blends "spiraling" riffs with a "rolling" drumbeat and jazzy piano. Stereogum compared "Colours Fly" to Radiohead's "Pyramid Song" and "The National Anthem," featuring an Egyptian scale and "clouds of noise." "Instant Psalm" includes strings, an "earthy" melody, and acoustic guitar, reminiscent of Radiohead's The Bends. "Tiptoe" is a piano ballad with orchestral strings.