As @Merriment and @mellow_girl said, a lot of times cutters are in such mental anguish—no doubt hating themselves and thinking they are shit—that some kind of physical pain takes the attention away from the mental pain. You can do stuff obsessively—scratching the same place all day long, for example—or you can do things like cutting, which, I imagine, focuses the attention on the activity and the pain, and lets you not focus on the mental pain. Suicide is often another result of such mental pain, so cutting is better.
What do you say? You show you understand. You can talk about times when you have been in anguish, and encourage them to talk about what is bothering them. A lot of this pain comes from unfathomable loneliness and a belief that one is utterly and completely unlovable and that one will never, ever be happy.
You feel lead in your stomach, axes attacking your back, the weight of hod of bricks on your shoulders, and your mind circles around and around, seeking a way out of the pain and never finding one. If you can imagine this, or a time when you have felt something like this, you can show that you understand, and that the person has company.
You can also try to offer love, but that can be very tricky. I’m projecting here from my experience, but they may try to push you away when you offer love. Feeling loved is not part of their world. It doesn’t makes sense. It’s a sham, and it won’t last, so rather than letting it in only to be disappointed (and expectations of love are huge at this point), it seems safer to keep it away. It’s only right, anyway, if you aren’t lovable.
So I think that consistency matters more than love. Just be there, regularly. Don’t leave without telling them when you will return. Return when you say you will return. If you can’t make an appointment, call or text to say so. Only behavior will convince them that someone actually cares. They see through words. Words mean nothing. Sometimes they don’t consciously see the behavior, but they will take it in subconsciously.
So, be understanding, and be consistent, and keep them informed.
They may test you by not being there when you come. Do not take this as rejection. It’s a test. Continue to be consistent.
It’s almost a full time job. Do you really want to be there for your friend?