It's easy to play armchair quarterback or absolve yourself from getting involved in a situation like this because
In circumstances of abuse it's
not the victim's choice. Who would sit in an abusive relationship and just take it? Almost everyone. "It would never happen to me" comes out of almost every victim's mouth. Victims of abuse do not have the context to understand their situation. They've been put in a place where their abuser has defined the terms of everything, and literally cannot understand what seems obvious to people who aren't experiencing it. It's not simply a question of willpower.
The fact that she'd turn down a safe place to stay with you because she "doesn't want to cause trouble" says that she's been devalued enough by this guy's actions that she feels like she deserves it. She thinks
she is the one who's fucking up, who's causing his behavior. It doesn't mean she's hopeless, it means she needs a lot of help to get the strength to accept a helping hand. Keep in mind also it often takes
multiple tries for victims to leave abusers, especially if there are children involved.
What can you do? Start reading and educate yourself on not only her particular circumstance but abusive situations in general. Talk to her friends. Everyone has probably noticed something but it's really easy to sit back and declare it not your business, either from reticence about breaking social mores or from denial that it's happening. If you can, (and make the effort if you can't right now),
talk to her family. A lot of times abusers, during their honeymoon phase, will get the victim to cut off contact with their support. Her family is probably concerned, if not frightened. Talk to
your friends. Tell them what you think is going on, especially if they know this guy too.
Also: he has threatened to SLIT HER THROAT.
CALL THE POLICE. This doesn't have to be for the purpose of filing criminal charges. Ask them for resources, for steps on what to do next, for suggestions. But do your part and make the police aware of this guy's name. This can be a dangerous circumstance; if the police take action, often abusers will take it out on their victims, but sometimes it's the only way to get the ball rolling.
From one of the articles below:
Here's some quick info so you can start learning about what's going on:
The Cycle of Abuse - a handy chart
Domestic Violence and Abuse - information much like Kohan's link
Women's Shelters - shelters by state
How to help a friend who is being abused - exactly what it says.
Safety Planning - Victims need a PLAN to get out. They're frightened, vulnerable, and often have no idea what to do because their lives have been controlled by the abusive partner. Help your friend plan.
More tips for being the friend in this circumstance - What to say/do, what not to say/do
Even more tips for helping friends in abusive relationships
Also, there is a hotline: (800) 799-SAFE. Call them and talk to them about the situation. They are trained for this.
[Note: I'm going to clean up the joking / bullshit responses in this thread. This is not the fucking place.]