Cutbush is a surname. Notable people with the surname include:
Edward Cutbush (1772–1843), surgeon, US Navy officer, professor of chemistry James Cutbush (1788–1823), American chemist John Cutbush (born 1949), English footballer John Cutbush (cricketer) (fl. 1740s), English cricketer Thomas Hayne Cutbush (1866–1903), London clerk, accused of being Jack the Ripper