I've cut carbons with a hack saw and mitre box. First wrap the area to be cut with a layer of masking tape to prevent splinters. Cut with gentle strokes and a fine tooth blade. After the cut, champfer the inside and outside edges ever so slightly with fine grit sandpaper.
If you need to square the end, lay the shaft along a piece of wood, 2x4 for example, that's cut square on one end. Move that piece of wood with the arrow back and forth on another flat surface to which you've attached some fine grit sandpaper. Best to do this horizontally so the table surface keeps one side of the shaft square and the block keeps the other side square/90 degrees to the sanding block/surface. Good luck.