Tell your boyfriend or girlfriend that they are still important to you, even though you're breaking up. Let them know that you don't want them to hurt themselves.  Say something like, “I still really care about you, and I'm sorry this is so hard for you.” You might also say, "It hurts me to hear you say you'll hurt yourself. Even though our relationship isn't working out, I still believe you are a wonderful person." Understand that they may not believe you when you say this. Let them know what you are willing to do for them, but do not feel pressured to do something you're not comfortable with. Don't challenge or argue with your boyfriend or girlfriend about their suicide threats. If they feel like you aren't taking them seriously, they may hurt themselves just to prove you wrong.  For instance, avoid saying something like, “You don't really mean that,” or, “You're just saying that to make me feel bad.” Instead, you might say, "I'm sorry that you are thinking this way." You can also avoid an argument by using "I" statements, such as "I am unhappy in this relationship" rather than "You don't make me happy," which may make the person defensive.  Keep your tone of voice soft and low. Maintain open body language with your arms and legs relaxed at your sides. When you raise your voice and use intimidating body language (e.g. crossed arms or balled fists), an argument is more likely to occur. Let your boyfriend or girlfriend know that you're not going to change your mind. Restate the reason why you want to break up. Be as kind as you can, but don't be wishy-washy. You could say something like, “I can't sacrifice my long-term goals to stay in this relationship, even though I think you're a great person with a lot to offer.” Tell your boyfriend or girlfriend that you can't control whether they kill themselves or not.  Don't let them push the blame onto you. For instance, if your soon-to-be ex says, “When I'm gone, it will be your fault,” you could reply, “I don't want you to kill yourself, but that's your choice to...

TL;DR in Vietnamese:
Nhấn mạnh rằng bạn quan tâm đến đối phương. Hạn chế cãi vã. Duy trì giới hạn. Nhắc nhở đối phương rằng lựa chọn của họ không liên quan đến bạn. Nói với bạn trai/bạn gái rằng họ không chỉ có duy nhất tình cảm này. Tìm nơi giúp đỡ người ấy.