His primary offence was that he used his blog to encourage his followers to harass D'Ozario. I haven't read the tweets, but even Sims admits he was a jerk. He engaged in this behavior for three years. I don't believe that threats of violence are necessary for this to be considered bullying. I have read that he made a comment that she should cut off her hands or something to that effect. But I haven't seen the comment myself, so I can't swear to that. I do know that he showed up on her site to gloat about the abuse she was receiving from his fans. He posted:
"You gonna to CRY, little girl?"
Whether or not Sims actually threatened D'Ozario, he went out of her way to make her miserable for three years! She actually dropped out of writing comics as a result. I don't think there's any doubt Sims crossed a line. Even he admits he did.
Edit: For what it's worth, DOzario doesn't want Sims to be replaced. She's afraid of being blamed for it if Marvel takes action against Sims.