A ply transporting and compacting apparatus comprises a rigid frame, a top-layer sheet of flexible rubber material fastened to the frame, and a bottom-layer sheet of perforated flexible rubber material having openings. The apparatus also comprises a middle-layer sheet of flow media material disposed in a first plenum area that is defined between the top and bottom layer sheets. The apparatus further comprises a moving device coupled to the frame and arranged to lower the frame and sheets onto a composite ply at a trimming location to pick up the composite ply with a suction force when a vacuum is drawn in the first plenum area to create the suction force through the openings of the bottom-layer sheet.