Minifigure Hand broken and stuck in arm
Don't fix it

I sympathize with the desire to fix it, but on closer consideration it doesn't seem easy or worth it.  Getting the hand out would probably damage the arm even if you manage to do it.

Replace it

The entire torso is available for less than $1 on BrickLink.  This is the easiest path forward.  Some similar torsos are half as much if you don't need an exact match.

There are replacement arms for many colors and color combinations on BrickLink, but not a plain blue arm like this that I could find.

If you get lucky.

Apparently you can buy just the hands as Mr. Shiny and New 安宇 pointed out.  So if you manage to get the hand out without damaging the arm you can solve your problem for a few cents plus postage.

Or re-purpose it

As with all of LEGO the possibilities are limited to your imagination:


maybe this soldier had his hand cut off and he's too poor to get a  prosthetic.
maybe this guy is holding a tray of drinks on his right arm during a battle.  I don't have an arm with a missing hand to test this, but I hope something could be attached to it.
maybe he had a tragic shaving accident and you can make a bloody scene about it.
maybe this soldier put on the wrong uniform and you can live with 2 new matching arms from BrickLink that aren't entirely blue.
maybe he's sticking his arm into a bee's nest or a hole in a dike.


So I hope you can see some way to get more value out of your "broken" torso than just tossing it.  But sometimes we've gotten all of the life out of a piece and it is time to let it go.