Old English screadian "prune, cut," common Germanic (cf. Middle Dutch scroden, Dutch schroeien, Old High German scrotan, German schroten "to shred"), from root of shred (n.). Related: Shredded; shredding. Shredded wheat is recorded fron 1885.
Old English screade "piece cut off," from West Germanic *skraudas (cf. Middle Low German schrot "piece cut off," Old High German scrot, "a cutting, piece cut off," German Schrot "small shot," Old Norse skrydda "shriveled skin"), from PIE root *skreu- "to cut, cutting tool" (cf. Latin scrutari "to search, examine," from scruta "trash, frippery;" Old English scrud "dress, garment;" see shroud (n.)).