Literally to amputate below the waist. It removes the legs, genitals, urinary system, pelvis, anus, and rectum.

If done surgically, it is possible to survive such a procedure, but it has only been done a few dozen times in recorded medical history. 

A traumatic hemicorporectomy where the patient survived has never been recorded.

The Argents use this as a fancy term for cutting someone in half with a sword.