The invention provides, in certain aspects, grafting devices deliverable into the body for repairing defects in bodily structure walls. One such grafting device comprises a compliant sheet-form material, and a removable resilient element that is retained in association with the sheet-form material. In some forms, the resilient element is adapted for delivery in its entirety into the body, and thereafter, can be disassociated from the sheet-form material for removal from the body. The sheet-form material may be formed with one or more of a variety of biocompatible materials including some that are naturally derived and some that are non-naturally derived. Illustratively, the sheet-form material may be comprised of a remodelable, angiogenic material, for example, a remodelable extracellular matrix (ECM) material. In additional embodiments, the invention provides methods and apparatuses for delivering these and other inventive grafting device into the body.