A novel dunnage-creating machine and methodology characterized by various features including, inter alia, a modular construction, easier access to interior components, and a low cost cutting assembly. The machine comprises front and rear units having separate housings. The housing of the rear unit includes an outer shell having a converging chute surrounding a shaping member over which sheet-like stock material is drawn to form the stock material into a three-dimensional shape. The front unit includes in the housing thereof a feed mechanism for drawing the stock material over the shaping member and stitching the shaped material to form a strip of dunnage product. The front unit also includes a manual cutting mechanism for cutting the strip to form cut pieces, which manual cutting mechanism includes a readily replaceable blade assembly.