He's just pissed because the bastard's talking about her like she has to be "owned" by somebody. She's not Hak's woman, but he does love her, and has owned up to that.
Now if only she could make it clear that she loves him too and make him actually understand that his feelings aren't one-sided anymore, then we can make some progress on this lovely relationship of theirs.
Also get her out of prison and him to a doctor. He's losing a lot of blood.
she has not yet said it directly enough for him to understand.
See, Hak has been dealing with his one-sided feelings for so long, he has come to the conclusion that any sign, any hint, no matter how obvious, that Yona shares his feelings are all in his head. Just wishful thinking.
It is a truly tragic condition. and can only be cured by blunt, direct communication between the two parties involved.
As you can imagine, it is quite rare.

HAK!!! JUST SAY IF SHE’S YOUR WOMAN, YOUR PRINCESS AND YOUR LOVER DARN IT!!
CLAIM HER N SHUT HIM DOWN!
ヽ(`Д´)ノ