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It disgusts me to write that subject but after all that we have done for our daughter to hear her say that she wants to break my jaw and kill me has threatened to permanently damage our relationship. How do I stop hating my child?

What has she been doing which resulted in you doing so much for her beyond normal parenting duties? Had she gotten herself into trouble?

 Hi Lpo

How horrible for you to hear that from your child!  You have a right not to be spoken to with threats or violence.

I think you will hate your child less if you enforce that she cannot speak to you that way.  I always seem to be answering with suggestions of consequences!  But I think they are important, that she has to pay some significant penalty for speaking to you that way.  I would suggest explaining as gently as possible (perhaps in a written note) that this behavior is not acceptable and what the consequence will be, and what she needs to do to perform restitution; then take away her electronics or something else she greatly values until she does somethign positive, such as extra housework, that helps you.  Then thank her and return her items.  That might make you feel better towards her.   I really like the concept of restorative justice, in which the consequence is not a punishment as much as restoring the hurt one caused.  

At 13, you have leverage over her since she cannot actually survive on her own, unless she is willing to take very great risks.  And if you give her a supportive environment but with firm boundaries, I think its unlikely she will take those risks.  So I would definitely apply the consequences firmly now before she gets to 16 and will no longer listen at all!  Once you feel in control, you probably will feel more positive towards her.

Once she has done the consequence or otherwise finished the task, try to give her extra attention and kindness, as she probably does feel badly.  But be ready to be firm immediately as soon as she slips up again, which she most likely will!  Cathy Glass has written a number of books about fostering kids who say and do horrible things because of their experiences, and how to get them out of it. One that I really like is Happy Kids, about how to reinforce boundaries effectively.

Good luck!  

I remember googling the same phrase when my daughter was 13, and yes she would say these type of things. I completely agree with incadove.  Reasonable consequences allowed me to feel like an adult and feel more in control.  We had therapists, psychiatrists and my husband who disagreed with consequences.  But, we also had very good therapists who believed in consequences.  One of the best sources of support for me was empoweringparenting.  You can google it and find their program.  They have very good advice on giving consequences that work, somewhat.  The truth is that her behavior did not turn around from those consequences but they did give me some peace of mind, they decreased the frequency of the bad behavior, and they set the stage for letting my daughter know my values and strength. 
My daughter was on a roller coaster for poor choices but somewhat functional behavior.  Last year she went to college, dropped out, lived in an apartment (we would not let her move back home) and supported herself.  This summer, she hit her bottom (which will always be different than what you think) and came back home to live with us as a changed person.  She is trying to do the right thing and it is such a blessing to have a nice relationship with my adult daughter.
Take care of yourself, build your inner strength, use consequences to set boundaries and let her know where you stand and understand that things may not turn around until she is an adult.  Role model healthy, kind and confident behavior.