Could there be any serious risk \aside from excessive blood loss\ to self-harm \wrist cutting\?

Yes: I've treated people who had this problem in their teens and early twenties who later in their lives experienced significant embarrassment and interference with job applications because of the permanent scarring, having to wear long sleeved shirts even on the hottest of days.

Cutting: If an artery or large enough vein is severed, and proper care is not administered in time, results can be serious, and even deadly.

Yes: Depending on the depth of the cutting - it can cause damage to underlying structures such as nerves, blood vessels, muscles, tendons, etc. If a scar forms - you may carry that for life. Please take care.