You can't dig out the last tile at the map edge.
You can, however, use the same method that flood-farming uses, and build an evaporation room. I'd also have an "airlock" system for filling the well cistern. And a locked lever room. And doors on the well-room.
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Side View:
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So, water enters from the river, and you open the leftmost floodgate(1) to fill the "airlock"(pictured empty), close the first 'lock, then open the second(2) to fill your cistern, and close the second lock; the cistern here dips in the middle to concentrate water as the level lowers through use.
If Timmy McEmo falls jumps down the well, you can open the cistern pit lock(3) to drain your cistern into the evaporation room, while the Cistern Floor Lock(4) provides access should Timmy's corpse now wash down into the evaporation room. The Evaporation Room Lock(5) + locked door provides double security and access to washed crap from the cistern.
EDIT:
Just make sure the evaporation room's floor area is atleast seven times the number of tiles in the cistern, so all that 7/7 water can spread out to 1/7, otherwise it won't evaporate.