Cut a Dash.

Make a show. Cut is the French couper, better seen in the noun coup, as a grand coup, a coup de maître (a masterly stroke), so “to cut” means to make a masterly coup, to do something to be looked at and talked about. Dashing means striking—i.e. showy, as a “dashing fellow,” a “dashing equipage.” To cut a dash is to get one’s self looked at and talked about for a showy or striking appearance.