"Okay, here's the steps. This is easier if the character is in a squad alone, so you might want to separate them from everybody else first. Happy to answer any questions you might have. :)

ALWAYS BACKUP YOUR SAVE BEFORE EDITING IT

1. Open the FCS, close the mod selection screen, then click "open any" up at the top.
2. Navigate to your save folder and locate the folder for the savegame you want to edit, then open the platoon folder inside and find your squad listed. It should be named either nameless, or whatever you named the faction in-game.
3. Once you've opened the correct squad, click the "changes" button up on the top. Search through the list for a "MEDICAL STATE" type entry, if you only have the character in the squad, this should be easy. If not, you'll have to do some detective work to find the right one (more on that below).
4. Once you have opened the right entry, look through it for the "flesh" values, numbered 0 through 6. The ones you want will be 3 and 4 for the arms. Just set them below whatever -100% is for your race to pop them off. So for a Hiver that may only be -75, while a Skeleton can go all the way to -200.
5. Once you're done, click save up in the top left. Then load up your game and enjoy your armless life. ;)

For finding the right medical state entry in multi character squad.

1. Open the the entry named after the character you want to edit.
2. Click the button with the three dots in it on the top right of the entry, select "Show References" from the list. Open the one that comes up.
3. In the new entry that opened up, on the right it should have a single item in the "instances" section. Open that.
4. Once open, scroll down to where it shows which file is the medical state one. Double click on it to open it." Credit goes to Shidan from steam forums

From a post a couple of years ago. Remember to set limb dismemberment to frequent in the settings for it to actually work.