Final answer:
Cutting the dorsal root of a spinal nerve is done to block the transmission of pain signals to the brain, providing pain relief.
Step-by-step explanation:
The purpose of cutting the dorsal root of a spinal nerve to relieve pain is to block the transmission of pain signals to the brain. When the dorsal root is cut, the pain signals from the affected area cannot reach the brain, resulting in pain relief. This procedure is sometimes performed as a last resort for chronic pain that is unresponsive to other treatments.