I did excatly the same with a cuttin disc sliced through my thumb & took a bit of bone off ! ! !

I was cutting through an exhaust manifold & the grinder jumped.
Had a flappy bit of skin hangin on & when you lifted it (which I did alot

) & my brother almost fainted ! Had to go lay down !
I got some blue role & insulating tape, wrapped it up & carried on ! Didn't stop bleedin for hours tho, but didn't need stiches in the end
Thing is tho, my best friend carried on cuttin & as the manifold was still in the car, he ended up going through a fuel line & the whole thing went up ! ! !

Oh me old dears drive way right in front of the house !
To say we weren't popular that day would be an understatement ! lol
Jb