The tool is just referred to as the cutting arm. It's part of the revolver armorer tool kit.
S&W makes their own by welding a bar to a trigger for the appropriate revolver frame (like a J-cutting arm for the DAO revolver armorer class). The hardened cutting hand is installed in the trigger like a regular hand.
I've only cut a couple of extractors. I found that both required no further fitting in order for them to give good carry up, but the class (and manual) does show you how to identify any long ratchets and use a Barrett file to dress them.
The revolver tool kit is listed in this S&W armorer tool kit link (scroll down the page) and shows the K cutting arm, although the took kit I received had the J-cutting arm.
http://www.smith-wesson.com/wcsstore...y/TOOLKITS.pdf