You are in a very difficult position because you do not have the authority to get these children to the help they need.

You say the families are aware that the kids cut, but you also say the families are  angry and threatening, and not psychologically helpful.  I do not get a sense from your question of your personal involvement with these families. You may have heard from the teens that the parents are angry, but I can't tell if this is fact or hearsay.  If you have not spoken with these families yourself, this is something that would be important to do.  In fact, some experts would suggest that you have a responsibility to speak to the parents/caretakers of these kids.
I would agree with that.

A youngster who is cutting, needs help and needs it right away. Cutting is a serious form of self-injury. If there is any possibility of your building relationships with the families of these teens, I suggest you do it. Within the context of relationship you might be able to encourage the parents to seek the professional help needed by their children.  

It is a wonderful thing to have engendered the trust of a group of teens.  As a minister you have a crucial helping role because of the relationships you have fostered.  I have no doubt that your respect, support and caring are very important to these kids, as evidenced by the fact that they have shared their cutting behavior with you.  However, it would be a true miracle if you could become a trained treater of self-injurious behaviors (SIB's) fast enough to treat these young people yourself. Cutters need help from providers trained in these matters. And the hard part for you is that the teenagers' safety must come before confidentiality--even before trust. Sadly, you cannot solve the problems that are causing the teens to cut. It seems to me that it is your responsibility to do everything you can to reach out to the people who have the right and responsibility to get help for these children, i.e. the parents and legal caretakers or the social services authorities.

If the parents are not receptive, that fact could be construed as neglect.  You do not say what state you are in, but it is very probable that in your state you are a mandated reporter of child abuse/neglect. You may have to report neglect (a parent ignoring an SIB) even if it disturbs your relationship with the teenager.  But please be advised, while reporting is not something any mandated reporter ever wants to do, reporting can have a positive outcome if the social service workers are able to bring pressure to bear on the families to exercise their right and responsibility to get help for their children. Depending on the state, the report itself might be enough to initiate the proper services.

I suggest you consult with your "supervisor" or superior minister about how these things are handled in your faith community, parish, or church.  Get advice, support and encouragement for yourself, and do what you need to do to get help for your young flock.

Bette J. Freedson, LICSW, LCSW, CGP