A device and method for obliterating or occluding a body cavity or passageway, in particular, the left atrial appendage of a patient's heart. The procedure can be carried out intraoperatively, but is preferably carried out percutaneously by use of a delivery catheter to position an occluding device adjacent a patient's left atrial appendage. The occluding device may prevent the passage of embolic or other material to or from the left atrial appendage by volumetrically filling the appendage, closing the opening of the appendage with an occluding member, or pulling the tissue around the opening of the appendage together and fixing it in a closed state.