You can take an axe and just lop them in half, that pretty much kills them....

We've cleaned them a couple of times before cooking but we tend to default to cleaning them afterwards. I haven't really noticed a difference in taste however I wasn't really paying that much attention either.

I agree that once you've had fresh crab it is impossible to eat that stuff from the store. Sort of makes you a crab snob....
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Time on the water is time well spent.