I think Degra's death and Persis's death are the most violent things I've seen in Trek. By violent I mean personally confronting as well as the act itself. Obviously an episode where a planet blows up contains more violence as far as how many die in the story, but violence on tv isn't about a numbers game. These deaths are up close and personal, they are visibly very painful and cause us to recoil at what is happening to the character.
Degra's death is particularly horrible because of the last words his killers says to him.
"I am going to find your wife and children and do the same to them. Your traitorous bloodline will end at the tip of my blade.
Persis's death is particularly horrible because it is at the hands of her lover and brother, who kisses her as he stabs her to death.
So, are these the most violent deaths in Trek? I can't think of any others as in your face as these ones.