you seem to have assumed a lot of things about your little sister here. people don't cut "because it's fun" cos you know what, it's not!

You want to get your sister help.

STOP judging her because that's totally what you are doing.
TALK to her about how she's feeling
Get rid of the preconceptions you have and actually pay some attention to your little sister. things may not be what you seem to think they are.