[quote=@Invisible Man]
Well, I'm pretty much fine with Jax blocking those with some going into him. I think a champion like himself has faced worse pain than that and has died on multiple occasions in the Summoners Rift, so it isn't too bad.
[/quote]
The champions on Summoner's Rift are explicitly not their real physical bodies. They take damage and die and recover because it's safeguarded by the magic of the summoning. When people die outside of the summoned environment, they mostly stay dead, barring Noxian/Zaunite scientific interference. When they're injured, it takes time to heal. That doesn't become an issue in League because League is a low-narrative video game.

Crisis City is not safeguarded. If a sawblade cuts into your limbs, it cuts your muscles, veins, nerves and maybe bones. It takes weeks to heal and months to recover. Jax can probably keep fighting despite the pain, but unless someone in Mahora is a well intentioned healer, this fight would most likely retire him from the whole "survive for a month then confront the Viewer" game.