A great article called Cutting to Cope that talks about teenagers and cutting.
First, we need to respond in love. All of the kids I spoke with said it was important for the adults in their lives not to "freak out" on them. As Christians we need to extend the unconditional grace and love of Christ to these kids, letting them know they are accepted. Kids who cut already feel unloved, unaccepted and unwanted. More than anything they need to know they are valued. Parents should remain calm, and build a trust with the kids so they know they have someone to go to in hard times.
A lot more great suggestions in the article. As always, CPYU does a great job in their research and writing about it to youthworkers.
I haven't had first hand experience with this, but it sounds like its almost inevitable the longer you work with students.
Update - 2006-02-06 - Article moved to this link.