Funnily enough; we are going through a similar discussion in our family just now (my 9yo niece wants to uninvite someone from her 10th bday party.) It is tricky and my sister has sought my counsel over what to do (god knows why as I have sons who, god love them, are like dopey labradors and don't seem to worry about this kind of thing.) But anyway! Here's what we worked through as a family.
For girls this age, their birthday party is often the only real social capital they have. It's an annual opportunity for them to flex a bit of social muscle and exert some power over friendship dynamics that are otherwise often outwith their control. So firstly, don't underestimate how important this is to your DD: make decisions with her and influence , don't dictate.
Personally, on balance, we managed to persuade DN that it would be a greater cruelty to uninvite than not to invite someone in the first place. The moral satisfaction comes in having the POWER to uninvite, but choosing not to.
At 10, the sands of friendship are constantly shifting and I imagine soon the girls will be off to different schools where opportunities will exist for new friendships to be made. This can be scary but also reassuring for girls who can sometimes be caught in an unhealthy or unsatisfying friendship dynamic. This feeling won't last forever. And it won't be the last time she feels left out of something in life. She is worthy and if someone else can't see that, it is their choice but their loss. Horrible sicky life lesson.
Also, who's to say that the birthday party needs to be the only big event in your daighter's year? Perhaps when schools break up for summer you can let her have some friends round for a "schools out" picnic/ slumber party/ whatever and she can control that invitee list more closely and perhaps this girl will be on it, perhaps she won't: again, your daughter has some power.
In my DN's situation there was a complicated situation (she joined the school midway through a year and was breaking into an established group where two girls were welcoming and one was hostile. My DN was desperate to impress the hostile girl despite her being foul to her.) Although in the end she didn't uninvite the hostile girl, it has been such a useful opportunity for my sister to explore behaviours with her daughter that can hopefully nip in the bud any "pick me" behaviour which could pass into her relationships down the line. Why do we crave the attention of people who don't deserve it, etc?
So my advice- talk with your daughter about the bigger picture. Although the party feels like the most important thing in her life right now, it is just a day. She has the entire rest of her life to work out who she wants to socialise and spend time with and she can do that wisely now that she knows that this girl just ain't that into her (however much that smarts and sparks the craving for retaliation). The best retaliation is to go ahead with the party as planned and then fade herself out of this girl's sphere if she wishes to do so.
Hope this helps. We honestly agonised over this for weeks. 
