Anytime CPS is involved it is a big deal. In El Paso they do a lot of irrationall things and they will at a minimum implement a safety plan that they will tell you that you have to follow. Contact a local attorney and discuss the case with them. I and others offer free consultations but you need to talk to someone before things get rolling with CPS and additionally to deal with the schools failure to stop or help with the bullying issue.
It may well be policy to notify CPS when the school as a report such as the desire to hurt oneself. I would not worry so much about the CPS investigation as I would push about the bully situation. While your son may be able to handle the situation right now by using his words to threaten action, it could be soon that he no longer feels that he can deal with what is being dished out. In order to hold the school accountable, you need to report each & every little thing that happens to your son by the same bullies. (You do not need to report frivolous incidents with other kids - "kid stuff".) I would put the complaints in writing and deliver them to the principal, with a copy to the head administrator. Your son has the right to be in a safe school environment. CPS will be greatly interested in the efforts you have made to protect your son, even despite the school's seeming lack of interest. (If you cannot get satisfaction from the school after giving them sufficient and full notice, I would hire a lawyer and perhaps see if that lawyer can get their attention. You might also talk with the bully's parent about the situation. The parent may not be aware of what the child is doing, and could talk with the child.)
Good luck to your son.