The surgical tool of a surgical instrument is configured to have a plurality of tissue-cutting edges circumferentially spaced by flutes disposed in an exterior surface of the tool. Each flute includes an aperture that intersects an interior chamber of the tool for conveying tissue fragments cut by the edges into the chamber. The chamber communicates with an interior passage of a rotating tube on which the tool is mounted. During operation, the tissue fragments (e.g., bone fragments) cut by the rotating surgical tool are conveyed into the flutes and through the apertures into the chamber for removal from the surgical site through the interior passage of the tube, while the instrument remains in situ for further cutting.