I think this referral is a very good thing.
If your stepdaughter is cutting herself then her problems are serious and she needs professional help with them.
Hopefully the mental health team will see all of your family, not just your wife and stepdaughter which might help.
For what it is worth, I doubt that your stepdaughter is trying to break you and your wife up. I think her problems are coming from within her , probably from her past experiences when she was "neglected" (whatever that means) by her father and stepmother.
Try to hang in there, it will probably still be a rocky road yet, but hopefully you will get some help to walk down it.