A hot-press deep-drawing forming apparatus includes a punch that constitutes a lower die and a die that constitutes an upper die. The punch has an inner-face forming surface that forms the inner face of a product, and a bent corner against which a scrap section S of a workpiece W abuts. The die has an outer-face forming surface that forms the outer surface of the product. A blank holder and a pre-forming die that clamp the scrap section are caused to move, together with the die, until the clamped scrap section abuts the bent corner. The movement of the blank holder and the pre-forming die is stopped after the scrap section has abutted the bent corner.