Yup:
http://io9.com/the-walking-dead-mid-season-finale-was-tragic-for-two-1665128603So. Let's break down Beth's actions here.
Was Beth trying to kill Dawn? I think not. Beth surely knows getting stabbed in the shoulder will not kill Dawn. She also presumably knows that Dawn is a moron and would almost certainly shoot her in retaliation for the flesh wound. So Beth had to foresee the potential consequences of her actions, right?
So what the hell was she trying to do? Get Dawn killed indirectly? Free the hospital from her idiotic non-control? Commit suicide by idiot? Whatever she was trying to accomplish — presumably getting rid of Dawn in some manner — weren't there many, many other ways to do it that didn't involve her almost certainly getting shot or potentially turning the hostage trade into a bloodbath?
We'll never know, because Beth is dead. The hospital staff is more than happy to leave things be, and Rick and the others somberly the hospital. Of course, Abraham and the others pulls up just as Rick's crew are exiting, so Maggie's reunion with her sister has a bit of a damper put on it, what with Beth lying dead in Daryl's arms and all.
I don't know what The Walking Dead's writers were trying to get at in the Dawn-Beth confrontation, but it did not work. At all. It required Dawn to make a dumb decision, which was irritating but keeping in her character, but it also required Beth to make an inexplicable, dumb decision of her own, and then tried to make us feel bad that Beth basically entered a lion's den and started poking the dumbest lion in there.