Actually the Mythbusters disproved this one!
In their very special pirate episodes, the Mythbusters tried to see if you can slow your fall by using a knife to cut the sail. Through various small scale tests, the MythBusters found that sails were not made in one piece, but in fact had a number of seams where the sail was folded over into several layers, making them harder to cut. Also, the sharpness of the knife plays a major role in the myth. If the knife is too sharp, the pirate falls too fast. If the knife is too dull, it would be unable to cut through the seams. In the full scale test, Tory attempted the myth himself by using a moderately sharp knife on a full-size sail. However, every time he attempted the myth, his knife would hit the seam and pop out of the sail. In the end, the MythBusters concluded that there is no possible way that a pirate’s knife would be able to be at the perfect balance between dullness and sharpness to safely cut through a sail.
BUSTED! Don't tell Lydia that.