Don't rotate the arrow in the lathe. use the lathe to drive the cutting disk. If the lathe is not long enough, make an extension. You don't hold the arrow in the tailstock, but hold the arrow parallel to the bed, with the "tail end" of the arrow offset from the centre of the lathe. You don't need rollers to support the arrow, just a smooth shelf to the arrow side of the cut off wheel, which needs to be thin, and driven at 25,000 rpm, a bit fast for a lathe or electric drill. Woodwork router, sewing machine motor drive, pulleys from a motor? Buy a "dremel", Aldi/Lidl have decent ones, and make up a cut off saw. There is plenty of inspiration on the web, but do be careful and wear goggles/facemask plus dustmask for the carbon dust. Even though my cut-off saw looks simple, it is well engineered in wood and the Dremel is a good tool, as is the inexpensive ebay sourced diamond disc.
http://s130.photobucket.com/user/wingate_52/media/Arrow Saw/P1020820_zps1d115333.jpg.html?sort=3&o=5