You say that every time he doesn't get his way he threatens. My guess is that he then gets his way. You wonder if it is a way to manipulate. If you feel manipulated, you probably are. Your son may be seeking power and finds that this response gets him what he wants.
How does a parent or a counselor work around this without endangering the child? I encourage you to change the way you present consequences and rewards.
You may already be doing this, but here goes: Before the dance (or event) have a family meeting to determine your expectations: homework handed in, chores done, room cleaned, etc. Then determine consequences (rewards): permission to go to the dance, on a family outing, a friend's house. This will give your son some control(power) over what happens to him. When "dance" time comes, you can say very matter-of-factly, "You cleaned your room very well this week so you can go to the dance," or "I'm sorry you chose not to clean your room this week, so, as we agreed on, no dance this Friday." Then walk away. Don't discuss it.
Another tack is to calmly respond to a threat, "You know that would be a terrible blow to me, but you still can't..." In using this type of reply, be careful of your tone -- be sad, but firm. If your son continues to threaten, again, with real concern, tell him that this threat is so serious that you will have to take him to be evaluated because you couldn't take it if he really hurt himself. Then take him to be evaluated for possible suicidal tendencies. This will cost, but most insurance companies will pay for the evaluation. This should stop you son's manipulative threats, or at the very least, give you the info and backing you need to solve the problem.
Of course, I always recommend a parenting class or group where you have the input of many parental experts!