If possible try and read about self-harm and what can be done to help. The role of family and friends is both difficult and important. It is important to try and help the sufferer learn to be in control of their behavior. It can 
be difficult to remain calm, and concerned, without being angry, trying to be in control yourselves or over compensating.
Self-help groups for families of sufferers can be very helpful and lessen the feeling that you are on your own. Remember there are professionals who find trying to help these clients very challenging and they only see the client once or twice a week.
Families should resist the temptation to apportion blame; this is neither the family’s fault nor the client’s fault.
I suppose in our society we tend to want to blame someone. When we see a toddler ‘throwing’ a tantrum in a public place what do we think? But most children by a certain age will not have these tantrums.
With appropriate therapy and maybe some medication, your loved family member will not have these cutting behaviours any more. It is a behaviour that causes distress, it is no ones fault.
Thankfully there are enough therapists out there wanting to help.