I have done this since about the second year I was sailing.
I was single-handing in high wind off the land, so there was only "nervous" seas, but plenty of air. The boat was sailing nicely and I had the tiller pilot on.
I stupidly went down on the lee side to retrieve dunked fenders as the boat started to cross an open estuary, and the wind was funnelled there to much higher speeds (I suspect 40 knots as it was already 25-28 knots). I had on neither tether nor PFD nor handheld radio, and we were welll knocked down, with the cold October water of Lake Ontario up to my hips. By arm strength alone, I crawled up to the coach house traveller and managed to release the mainsheet, which flew out with such speed that it took part of the flesh on my fingers with it (Yes, now I wear gloves, as well!). The boom went out and the boat found her feet, and I spilled air until I could tie up my hand and continue. The autopilot had simply been overwhelmed at that point.
Had I a knife on me , I might have had the option of cutting the mainsheet instead of releasing it from an awkward "too close for comfort" position. I had plenty of line on board to rereeve the blocks and to get back to sailing.
Later, after I started to carry a knife, we rounded a point with an old No.1 up and again, the wind went from 8 knots to 22 knots very quickly. The leech line of this sail hooked on a spreader end, making it difficult if not impossible to douse (hank on sail). Going off the wind didn't help...the leech line was somehow hooked deeply into there (yes, I now tape off the spreader ends.)
Once the sail began to rip, I got out the knife, told my seven-months-pregnant wife to "feather the main close to head to wind" and stood on my toes and cut the leech line. I was then able to drag the mess down and we sailed into our basin under main only.
I have also cut off a piece of line that threatened to foul a moving prop, but that was on another boat.
As can be seen, inexperience or lack of anticipation led in part to bad situations, but there's a place for a small, sharp knife on board any boat, I think, and now it's habit for me to carry an inexpensive sailor's knife (serrated edge) on my belt, plus an inexpensive multi-tool. I use the multi-tool far more often as I am forever tightening bolts or screws or other fasteners both above and below deck. I go "inexpensive" because it's not tragic if a ten-dollar knife or multi-tool is sacrificed to Neptune.
I am aware that slicing a loaded line brings its own issues, but I still believe that lines are cheaper than limbs, and sometimes you have a need to cut away a line to save limbs, life or more important parts of the boat.
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