They don’t explicitly say how he survived, just that he was able to grab onto a vent as he was falling, kept himself alive through his immense hate for Obi-Wan and Palpatine, and dragged himself to a garbage skiff and got dumped on a junkyard planet where he went insane until his brother found him.
I’m gonna assume that the lightsaber cauterized his wounds and kept him from falling apart. And who knows what the differences are in Zabrak anatomy. Maybe bisection isn’t too big a deal for them, especially when the Force is involved.
I mean in a universe where someone dies of a broken heart, you have to admit that this isn’t that far-fetched.
In all fairness, Darty Vader shouldn’t be alive after being burned alive by lava and inhaling so much ash. I don’t care how high tech your robot safety suit is, real world, that’s not gonna happen. At the end of the day it’s a fantasy. Some suspension of disbelief is required. As long as it’s not stupid like dying of a broken heart, I’m willing to accept some far fetched things.