To act in a deranged, reckless, or unconventional manner. Refers to the eponymous character of the novel Don Quixote, who tosses his hat over a windmill (which he imagines is a giant) as a challenge to it. Sarah is always trying to buck social conventions, throwing her hat over the windmill whenever possible.I know you like to take risks in business, but don't throw your hat over the windmill.