This morning, a very dear friend of mine announced that they would be going to rehab so they could stop cutting. While sad that I wouldn't get to hear from them, I was happy to see them be able to get much needed help. But just half an hour ago, they came home. Apparently their mom pulled them out, so they wouldn't be staying after all. I feel horrible for them. I was hoping that going would be able to help them and make them happier, but their mother won't let them stay. Even though they are still weeks away from turning 15, they've have been cutting for years, and I was hoping to see them well. I wonder what I could do to be supportive of them at this point?

Not sure why you used 'them' as I'm sure we can't figure out the identity of your friend simply by using gender specific pronouns, but there honestly there is nothing you can do. All you can do is to be there to support your friend in any capacity that you can, but it is not your job to be helping them seek treatment. It is also not your place to talk to your friend's mother. Just being a good friend and offering to listen is more valuable than you think.

Do you know the reason why your friend was pulled out of rehab? And whether this friend had permission or consent from their mother?

I'm not sure how much support they could gain from it, but... tell them about The Butterfly Project? It's specifically meant for people who are trying to stop cutting.

If they are harming themselves and their parents aren't getting them medical attention, that's child neglect/abuse and you need to report it to the authorities (CPS, police, etc) so that they can get the help they need before it's too late.

Honestly, you could just report your friend's family to CPS and they'll force them to have your friend to go to therapy, and it's child neglect/abuse, so your friend's parents could get into hot water due to it.