Try to be very compassionate with this girl. She probably doesn’t have any friends, because of the way she comes across, just as you have said, but because she doesn’t have any friends, she has absolutely no idea on how to be an interesting, fun, regular person. Even though she’s a pain in your behind, you’d be doing her a huge favor to mentor her to be a more approachable and pleasant person.
You don’t need to tell her that she’s a big pain in the behind (at least not directly, because to do that would be horrible, mean and insulting, without actually helping her).
What you might consider doing, is letting a few of your nicer friends know what the situation is, and ask them if they’d be willing to join you both for lunch, so there’s a group of you, rather than just you. Make sure that these other girls are willing to be nice to her too, but show the girl by example, how regular friendships are supposed to work.
If she starts in on one of her downer rants, then you or one of the other girls can nicely say something like, “Hey Maggie, I know that XY and Z sucks, but it’s kind of a downer when you complain about it all the time. Have you ever tried to fix that situation or walk away from it or ignore it? Is there anything we can do to help, because I know how much it sucks to have XY and Z happen.” And if she persists, or brings up her complaints at a later date, say “Maggie, dude! Come on, we know already. Let’s talk about the dance/weekend/cute boys/new song etc. instead.” Get her engaged in some other conversation. If you do that regularly for awhile, she’ll get used to it. Just avoid any urges to be mean to her.
Give her at least 5 chances (and do not be mean or snarky to her). Sometimes people who have poor social skills need to be shown by example how to act in acceptable ways.
If you simply cannot get her to change, don’t tell her that you’re dumping her, just start seeing less and less of her, by having real reasons for why you can’t hang out. But try my other method first, before you just walk away. You could really do this poor girl a huge favor by treating her kindly, not dropping her like a hot potato, and including her in your social group.
Nobody says this girl has to be your best friend, but imagine what it must be like to be in her shoes. She’s probably desperate for a friend. Be a friend, but mostly be a mentor. And know that being her mentor does not mean that you have to be at her beck and call every minute of the day. You can easily set some limits (but give her good concrete reasons for why you can’t hang out, or chat on the phone all the time, so she won’t constantly ask you why. Use your parents, your chores, your home work, your alone time, your time that you spend with other friends as reasons not excuses).