To see an umbilical cord in your dream represents your lack of individuality. You may be expressing some anxiety about being on your own and supporting yourself. Alternatively, an umbilical cord symbolises your maternal ties. Perhaps you are too emotionally bonded to your mother.
To dream that you are cutting an umbilical cord indicates that you need to be self-sufficient and stand on your own two feet. It is time to pull yourself back up and get back into the swing of things.