Cutting is a form of self-injury (aka nonsuicidal self-injury - NSSI). In my, albeit limited, experience, most cutters are or have been victims of abuse, often sexual abuse. These patients usually are receptive to discussion about their cutting and its causes. Viewing these lesions may be an opportunity to show compassion and understanding for these patients.
Cutting, almost always, is a sign of "Adverse Childhood Experiences." These, ACEs have negative impacts on one's health as an adult and are well described in a New Yorker article, "The Poverty Clinic."
For more on cutting:
Why People Hurt Themselves
The Poverty Clinic by Paul Tough. There is a full text pdf online which I can not link here.
If you encounter a person with acute cutting, Brief Therapy Heals Trauma in Children, by Jane Brody, is worth reading.