I recommend 1 Watt 405nm labby on an adjustable mount with a 10x beam expander.
With this setup it should completely cut through a 1/2" diameter rope at 100' in about 5-7 minutes. Note: You have to slowly move the laser across the rope during the burning, and minute adjustments at that distance may prove to be almost impossible without a beam-table mount with fine x-y-z adjustment.