After 4 years in the Navy, and as "line Captain" on sea and anchor detail. I can tell you that it is very possible for a snapping line three or more inches in diameter to take off a limb.
Our lines had a small line woven into each end that was an indicator of whether the line was in danger of parting. We called it a "Tattle-tale". I don't know if you are familiar with the docking process. But there are six lines securing a ship to the dock. Three forward (1-4 inch line and 2-3 inch lines), with the same number aft. Most of the time the larger aft line (4-inches) is sent over first and a capstain (a huge winch) is used in conjunction with a tug-boat to get the ship near the pier. The number 4 and 5 lines, and the number 2 and 3 lines cross each other going to the pier to prevent the fore and aft movement of the vessel. Lines 1 and 6 go straight to the pier and are the larger lines, 4 inches in diameter.
As a recruit you are taught three things from the jump. How to fight fire, how to follow orders without question, and that a breaking line can take off a limb if it strikes you.
For a graphic view of this, see the movie "Men of Honor". The injury sustained by the character played by Cuba Gooding JR. is a very real depiction. I wouldn't be suprised if that scene becomes a part of the training curicullum for Boatswain's Mates.
I saw a tattle-tale break once, on a 4-inch (diam.) line. I can not emphasize enough the speed with which we cleared the fantail.
By the time the Chief that was in charge of the fantail hollered "Clear the deck" we were ALL on the Flight deck (one deck up) looking down at the chief.
For the record it was pretty stupid to wrap an arm in the rope. Especially with approximately 600 people on each side. If all the people on the team weighed in at 150 lb. that's about 90,000 lb. of weight (45 tons) on each side of the rope, not even counting the pulling force exerted by each person. That's just stupid!!