Speaking from the perspective of someone who self-harmed as a child, telling your DC to stop won't help. Self-harm is like an addiction, you can't just stop and knowing that what you're doing is hurting the people you care about can make you feel worse, which can in turn make you want to self-harm more.
I would echo blimppy and say if you haven't made an appointment with your GP, do so and if your child is talking of suicide, take them to A&E.
YoungMinds has parent helpline which may be useful for you and a lot of information. It might be worth doing a quick search for any support groups in your area too.
Try to stay as calm as possible when talking to your child about it, I know it can be really hard, but it will help so much. I know when I was in a bad place, distractions helped a lot. Going out for walks, watching something on TV (as long as I had something to fiddle with while I was doing it), colouring, my cousin still swears by paint by numbers. Encourage your child to spend as much time in the same room as you even if you're not talking, that can help.
My cousin found that squeezing an ice cube used to really help her, or putting an ice pack wrapped in a t-towel on her face/putting her head under cold water.