In my post above, the grab n go hook would be used instead of an anchor as you described, and with no topside damage. Once hooked, the snubber line it's attached to would be winched up. Still, I don't disagree with any of that strategy, and the hookknife looks pretty scary but effective.

I suspect you either got hooked to a whole string of pots, or the trap you hooked to got snagged under a ledge. In my experience when we snag one it usually just slows us down, unless the wind is light, but in almost every event there is a lot of tension on the trap line if you're snagged. The initial concern is damage to the boat's propulsion system, and the line cutter can reduce that chance. It should be able to handle the typical 1/4-3/8 lines used on most traps. But if you encounter wire or cable or loose nets you're probably SOL.

Another benefit of a line cutter is less likelihood of damage to saildrive shaft seals or damage to cutlass bearing from stray monofilament. What do people do with stripped line from reel backlash? Thoughtful people put it in the trash. Thoughtless people toss it overboard. Sometimes people snag a line on bottom structure and just cut it, so it streams in the current until it's crossed and snagged by a prop.