What can I do if my ex starts threatening me he'll hurt himself if we don't get back together but I don't want to get back with them?

That's should be a sign that he's trying to lead you into an abusive relationship. If you don't want to get back together with him, then don't. It's very simple, most people who say they'd hurt themselves if you don't get back together with them are usually bluffing. If you feel that he isn't bluffing, just tell some kind of adult.

first of all, going back with your ex is never a viable solution, it will make you unhappy and guilty in the short term and it will hurt you both in the long term, since you would be dealing with a person who is emotionally instable and not being able to be happy or comfortable around the other, and your partner will sooner or later notice your real feelings towards him/her, making themselves get worse. the ideal case is talking to that person's friends, family, or whoever both of you trust to speak with your ex and help him/her meditate what they are about to do and whether they need professional help to get out of this behavior or not. the actual issue, comes when this person has no other person of trust but you, in which case you may want to try to help your ex (as a friend) or strongly suggest your partner to seek for professional help. the important things to take into account when someone really close to you threatens to hurt himself is that following their demands does not help either of you, and that the guilt and the preassure may be dangerous for your well being, so never stop watching out for yourself no matter how important that person is or used to be for you.

If you ex needs mental health help, encourage them to call 911 if they are suicidal or another organization for those with mental illnesses. There are many resources listed on this site. If your ex is doing this to keep you together, this is not healthy for you and could be a mental game trying to get you to stay with them. This could possibly be your ex manipulating you through mental extortion. Would you be willing to give your ex resources in case they actually do need help? Could you set appropriate boundaries and be consistent with these boundaries so that you can stay safe and healthy and since you do not want to get back together. I hope this was helpful in some way.

you can't let him guilt trip you into getting back with him if that's not what you want, refer him to a help line

First and foremost, YOU are responsible for YOU! Your well - being comes first. If your well-being is not threatened by taking action of some sort, getting them in touch with resources (hotlines, etc) and support could be appropriate. But that's if and only if doing so won't risk dragging you into a situation that carries risk for you and is likely to turn uglier than it already is.

If your ex threatens to hurt themselves if you don't get back with them, you should find them some help. Talk to their family or find them professional help.

You should speak to someone about this, whether it's taking advise from local authorities or confiding in a parent or friend.

This is pretty simple. Be very clear with this person that if they make a serious threat like that, you will have to call the police.

He's emotionally blackmailing you. Try to explain it to him but if that doesnt work then block his ways to contact you

This is manipulative behavior, and I am glad you have identified that. I would recommend speaking to a trusted family member or authority figure; healthy relationships are never based in manipulation or deceit.