The periosteum is one source of precursor cells which develop into chondroblasts and osteoblasts that are essential to the healing of bone. Other sources of precursor cells are the bone marrow (when present), endosteum, small blood vessels, and fibroblasts.
Since mitosis is the division of cells, in this case, skin cells, it allows the dead skin cells to fall off. Also, mitosis can fix any injuries. Without mitosis, these things would not happen.