
I also think that Sangwoo might just messing with Bum, pretending to corner him and see his reaction because he wasn't satisfied with the uncle's story. It was boring, didn't match his expectation and a waste of time. I agree that Sangwoo was quite patient considering everything wasn't going well that day.
Since I don't think Sangwoo have any emotional investment towards Bum, he might find Bum's cutting the wrist amuses him or just pretend to be shock and be very sympathetic instead.

Yes, he might not be emotionally invested in Bum. But still invested in him in some way. I think his shock is genuine, but since this is Sangwoo, I also think he'll recover from it quickly and be amused too. He might hover around Bum, satiating his curiosity more than anything. That's the prediction closest to canon that could happen.
But another reaction that I could think of is that he'd be pretty pissed. How dare Bum, his property, do that without his permission? Or something along those lines. The slice was pretty big, lots of blood was lost and Bum's not exactly the model of good health good stature. I'd be a happy to see a pissed, panicked and frustrated Sangwoo struggling to keep someone alive. It'd be a lovely change. He's disposed bodies before, and have dealt with the dead. But I wonder if he had struggled to keep someone alive before?

I agree, that moment when Sangwoo decided to keep Bum alive is already an investment. I forgot that when Bum's missing he was already panicking and lose his composure. Maybe Bum's cutting his wrist and dying could trigger Sangwoo's past event that hasn't been revealed yet too. Chapter 27 is full of possibilities.
When I read chapter 26, my heart broke for Bum.. Someone needs to protect this poor child. And Sangwoo is just standing there, gawking at him like an idiot.