My theory is that Adolin killed him. Yes. I hear the cries that he didn't--there's no way! But there is.
What I think happened is that Sadeas was innocently walking down the halls of Urithuru, when he happened upon a wild Adolin. He started making all sorts of not-so-wise-cracks, and Adolin Snapped. He went crazy and started to lick the walls, made, of course, of Tanavastium. When burned, and Adolin burned it, it makes you go Spike-crazy. Honorably, of course. It was time to turn Sadeas into an Inquisitor.
But there was one problem--He had no Spikes! Or did he...
The knife was indeed a Spike. He had killed many a foe with it. And so, he rushed up to Sadeas and planted it in his eye. The Steel knife had killed the Parshendi, who had (obviously) Allomantic physical powers, and granted him the power of steel. Which, on Roshar, grants you the ability to Push off of Gems, using Stormlight as fuel.
Oh. Also, Adolin happened to be a Soother, and took Sadeas' body over with a strong Push.
The Spike in Sadeas' eye forced away his bonded Shardblade, and it puffed into existence with mist. Adolin drew upon the Mists. And commanded Sadeas to kill Szeth--to Spike him with a knife into his other eye--to steal his Surgebinding powers. Only, Szeth didn't have a knife on him, so Sadeas was forced to use...
Discuss.
(Oh, and Adolin obviously realized that if he planted Oathbringer, Cultivation would cultivate it to grow into a magnificent Shardtree. The most awesome and terrifying trees of all, that grant strange and unknown but totally real powers to all.)