I have a rod of tool steel that is 3.1mm square. I need a 2.5mm square rod to use as a mandrel for fabricating a setting for a square gemstone. I can file down the rod but that is laborious. Is it OK to put a tool steel rod in a rolling mill? If it’s doable, should I anneal the rod first? Thanks for your advice.
You could anneal a square needle file (just get it red hot and quench it) and then file it; probably easier than filing a round rod and you’d know it was good steel. Also, the needle file would have a bit of a taper which might be helpful.
Rather than filing, consider an angle grinder. You can take that rod down to its required dimensions in no time. I have gotten good use of the one I got at Harbor Freight over a decade ago. Its about $40.
Quenching the steel from red hot will only re-harden it. Tool steel needs to be cooled as slowly as possible after heating to a red heat. It is frequently done by burying it in an insulating material such as perlite. Can also be done in a kiln, slowly dropping the temp from ~1450 - 1650 Deg F. Google “annealing tool steel” for more detailed info.
I think running a piece of tool steel through a rolling mill is a recipe for disappointment. I suspect you won’t get the results you want and you will get to buy a new mil.
I would heat it up to a nice color and hammer it out to the desired size. File it to a finished size and then harden it.
Working with tool steel is a very interesting study. There is a lot of procedure to follow for the finished result. Unless you plan to work with it often it may be less expensive, time and cash wise to buy a new mandrel.