It's soooo hard, but the thing that works for my potty mouthed teen is to IGNORE HER when she starts talking like that. One blue word gets a very calm warning: "Please stop swearing. I can't have a conversation with you if you are going to talk to me like that." If another one comes out of her mouth, I just calmly say "When you are ready to speak to me without swearing, we can talk again" and then quietly get up and leave the room. Do not engage in conversation until she is prepared to do so in a calm, polite, respectful way.
They can't explode when there's no fuel. If you get upset and hit her, it justifies to them that they can yell and scream and hit and get a reaction out of you. Do not give them the satisfaction of a reaction.
They want you to get angry with them for swearing. They want you to add fuel to the fire. They want the confrontation to escalate. They get an adrenaline rush out of it, like a drug fix. It makes them feel powerful to make you lose control. If you remain calm, you do not lose control.
Things that teens value at this age are independence, money, control, money, computer access, cell phone access, money, access to friends, money, recognition (feeling valued), and money. Find out which of these things she values most, and offer to work with her to help her acquire the things she values.
If she loves having friends over for sleepovers, give her a goal: When we can have conversations for a week without her swearing at you, then she can have a sleepover. If she likes buying her own makeup or renting movies or buying CDs, buy a $10-20 gift card for her favorite store and tell her she can have it if she goes a week without swearing at you. If you want to work on a more long-term goal, a month's worth of freedom from her potty mouth can earn her a trip to her favorite shoe or clothing store. If you think she's mature enough to handle it, tell her she can earn a pay as you go cell phone for her next birthday if she can go six months without swearing at you.
I also think that there's a difference between a teen simply using swear words in conversation and using those words as weapons to assault another person. I will not allow language that constitutes a personal attack or an insult. If they use common expressions like "that's $h!tty" or "that's f***ked up" I will say that I prefer that they don't use language like that, but I don't make a huge issue out of it. I appeal to their vanity, and say "It makes you appear so much more mature when you can get your point across without using that kind of language." However, when they start insulting people with those words I draw the line and they know they will have consequences.