Anchors resist a sideways pull. When anchored you have enough anchor rode (rope and/or chain) for at least double the depth of water. The weight of the rode makes it form a curve called a catenary which means that at the anchor the pull is almost completely horizontal.
Then when you want to raise the anchor you pull in the rode until it is straight up and down. This rotates the anchor and breaks it out of the seabed without much resistance.
As for avoiding getting the anchor stuck in rocks, the trick is not to anchor in places with rocks. A lot of seabed is mud, sand, shingle etc.
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