For removing this dead skin, doctors follow a procedure known as debridement, which is done through surgery and other non-surgical methods. The appropriate method for debridement depends on the severity, size and the shape of the wound. Examine your wound. Look for signs of wound turning black or gangrenous. Contact your doctor immediately if you find the skin around wound appears dead and black. According to Amputee Coalition of America, your skin turning black is a sign of infection, which requires “emergency” attention of a doctor. The doctor will prevent the infection from spreading to other body parts.