I was taught, many years ago, to use a fine triangular file. Just support your threaded rod in some 'soft jaws', and file around the cut line. After you have cut around and to a depth of about 1/3 total of the rods diameter,(3 or 4 passes), the rod will usually snap off at the cut line, with a bit of a bend.
This method leaves a bit of a bevel, (good for starting threads), with a circular, grainey tip, which be dressed off with a fine flat file, to the desired depth of bevel.
This is the method I use, as well, for cutting metal pipe and tube, regardless of diameter.
I hope this is of some help.
Glenn.