You shouldn't stay with someone because they've black mailed you into staying with them. Just be calm and as empathetic to her as you can be when you tell her that the relationship is not working out, that you're not compatible enough to remain together any longer and then don't contact her anymore. Go zero contact so that she has a chance to heal from her attachment to you. Call a suicide hot line if you're worried and ask them for tips. Encourage her to get the help she needs. She needs therapy if she would even say she'd kill herself if you leave her.
DO NOT go running back to her if this new relationship you've been cultivating while still with your current girlfriend does not work out. That would be very cruel of you.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion