In the common situation where the anchor is hung up on the bottom, you just pull in the chain tight, even to the point of dipping the bow a little. Then cut it off with whatever tool you have.
I once got my anchor stuck and was about to do the above when it finally pulled loose with a kind of muffled screech. It was hung up on a piece of metal and I finally pulled at the right angle to get it off.
David
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