"cast off," Old English sceadan, scadan "to divide, separate," strong verb (past tense scead, past participle sceadan), from Proto-Germanic *skaithanan (cf. Old Saxon skethan, Old Frisian sketha, Middle Dutch sceiden, Dutch scheiden, Old High German sceidan, German scheiden, Gothic skaidan), from *skaith "divide, split."
This is probably related to PIE root *skei- "to cut, separate, divide, part, split" (cf. Sanskrit chid-, Greek skhizein, Latin scindere "to split;" Lithuanian skedzu "I make thin, separate, divide;" Old Irish scian "knife;" Welsh chwydu "to break open"). In reference to animals, "to lose hair, feathers, etc." recorded from c.1500.