If she is telling you to kill yourself, I'd bring it up with the police. She's threating you.

Feelings come from within and there's always a reason why someone behaves as they do, so there's a reason your sister treats you this way and that reason has to do with something in her life. People who try to make others miserable tend to do so because they are miserable themselves. Projection, which is when you tell others things apply to them that you believe deep down apply to you, is incredibly common among humans, so she may believe she doesn't deserve to live. In that case, you'll need to talk to her and be patient because it may take a lot to get through her layers of pain and defensive barriers she's putting up. No matter how she treats you, be kind back. That removes her ability to keep at it without guilt eating away at her. If indeed somewhere in there she is hurting and is taking it out on you, she needs to know you care despite what she's done and that you forgive her. Let her know it hurts you, but that you love her anyway. In time, love eventually breaks through hurt.

The other possibility is that she doesn't take her words seriously or believe you're really that affected by them. That would be the case of her thinking it's just part of being siblings. In that case, she needs to know how it hurts you. The emotions she needs to see are your pain or sadness. Anger tends to make people defensive, so if you are angry, she will try to justify what she's done. But, if you show your hurt so she can see it but then actively forgive her, she will be more open to learn. You can also model how she should treat you by treating her how you would want to be treated. Humans tend to treat others how those people treat them, like being angry with someone angry at us, so model kindness and eventually with time and patience, she will subconsciously start to change and you'll see her act differently. But, remember, it all starts with talking to her, no matter which of these is the cause of her behavior. And, maybe she won't open up, but that's just protecting hurt.