RSS
There are so many possible explanations for weird stuff in your campaign that honestly you don't need to come up with any specific justification. Merely present it boldly as incontrovertible fact.
However, if they call you out and ask how it works then you mustn't shrug your shoulders like you don't have any clue (even if you don't). Just confidently declare that there's a sensible explanation in the background lore of the setting. And watch your players do the work for you by speculating a dozen different reasons that are plausible to them.
Commentary by memnarch (who has not seen the movie)
Aww, no lightsaber through hand. Maybe the arm loss happens later or even in the next movie then. It will be rather surprising if that plot point gets skipped in the Sequel Episodes.
This contest is more like an evenly matched Force Tug-of-War than a Force Arm-Wrestle. And since there's no rope to pull the contestants one way or the other, they can just slide apart as the contest goes on. Jim probably still has the more likely answers here though for something more than "the writers thought it looked cool".
Transcript
GM: As you both pull on the sword, you slide apart from the induced pressure.
Rey: Hang on. How does that work? We’re both pulling the sword. We should be pulled together if anything.
Poe: It must be like elastic rebound!
Kylo Ren: Like what?
Poe: As opposing forces across a fault line build over years, the land deforms and stores elastic strain energy.
Poe: Until local energy density exceeds the rock’s tensile strength. It slips, and the rebound pushes the strata apart.
GM: Mmm, yeah. That’s—
Poe: Or maybe like a salt dome... The sword’s buoyancy is driving surrounding material apart.
GM: Yeah, okay, that—
Poe: No, wait! It’s more like frost heaving! The Force is undergoing a phase change expansion.
Rey: Force heaving?
Kylo Ren: I’m just glad it’s not sulphurous gas buildup.
Poe: Oooh!!