To lead with: while it probably feels like this is extreme and impossible to deal with, we all deal with things that are not all that different as parents. Particularly if you're trying to parent in a manner that's not authoritarian, but is more in the modern vein of trying to help your child make the right choices on their own, there will be plenty of times when they just don't want to do what you want them to do, and since you're trying not to be authoritarian, you feel like you don't have any options other than authoritarianism - but that doesn't work well on a kid who's not used to it.
As you say, obviously yelling isn't an answer here. One major thing is to not take personally any of the things she says to you. "You're a bad parent", "I hate you", etc. - they're hurtful, but she's saying them because she doesn't have the right vocabulary to describe what she feels. What they really mean is "you're not hearing me" and "you're restricting me".
One of those things you can do something about; the other you can't. You do need to restrict her choices to some extent, because she has to do the homework. That's unavoidable - you're not doing your job otherwise! But the other - "you're not hearing me" - you absolutely can do something about.
Start with, "I hear that you're [emotion]. Let's talk about that." Frustrated, sad, angry, whatever matches her emotion right then. Then ask her open ended questions - and ask these legitimately, not just pro forma - about why she's feeling that way. Find out what the problem is. Probe. Get to the bottom of exactly how she's feeling and exactly why.
Then, see what you can do about those issues. Obviously, the answer isn't "stop doing homework" - but it may well be that you can get to somewhere that she feels okay about doing the homework. Or you may be able to give her some perspective.
Here's an example that is more or less how a similar conversation happened with my nine year old (but it could've been nearly identical at six). We'll use the name "John" for anonymity.
Aaaaaa, I don't want to do my homework. Homework is stupid.
I hear that you're frustrated with your homework, John. Can you tell me why?
Because it's stupid.
Hmm, can you tell me why you think it's stupid?
It's too easy. And it takes too long. And I don't learn anything. [John is probably 2-3 grade levels ahead in Math, so this isn't totally wrong.]
Well, if it's easy, it shouldn't take very long, no?
It's easy to DO but it still takes like HALF AN HOUR! I won't get any time to play iPad at all!!
Fair enough, sometimes things can be easy but still take some time. I know that it feels pointless, but there are reasons you do homework, even if you do know the material really well. Eventually you will get to a level where you don't know it very well - and you need to learn how to do homework. It's also how your teacher finds out how well you know the material - even if you know almost everything from third grade already, you might miss a thing or two, and then she can help you focus on those things.
But it's going to take FOREVER! I won't get my iPad time!!
I know it seems like a long time. But we won't get any iPad time if you don't get it done, and I think we have almost an hour and a half right now until dinner - so there will be some time. What do you think would help you get started? Do you think a snack would help? I'd really like to play some Minecraft with you afterwards, and we're using so much of our time already...
I want a snack.
Okay, we can go get some [snack]. Then let's get started on that homework!
The point of this is to do two things: we find out what the real concerns are [frustration from having to do things that are not right level, and being upset he's losing out on fun activity]. Then we try to address them: explain the reasons for the homework, and make sure he knows he's going to get to fun activity. Plus, add in an extra bonus [playing with Daddy]. Finally, we add a snack in there, which accomplishes two things: if it turns out some of this is low blood sugar, it takes care of that, but more importantly it provides a natural "cutoff" between the upset screaming and the actually-doing-homework.
There's no magic answer, and don't expect anything to work instantly - the point here is to help her learn to trust you and learn that you're listening to her and care about what she feels and thinks. That doesn't mean you let her do what she wants to, because she does have to do the homework. But it means you explain why, take her concerns seriously, use all the active listening tools you have available (repeat back, for example, is a great one), and try to consensus build.