Meaning of the phrase "squeeze water from a stone"

I agree with Barrie (+1) that the most usual idiom is blood from a stone. Water from a stone is likely a malformation of the standard idiom. There may also be regional differences. For example, I've also heard "blood from a turnip".

There is also a fairytale about a giant slayer who challenges a giant in a feat of strength — to squeeze water from a stone. The giant picks up a boulder and squeezes with all his might but cannot produce water. The 'giant slayer' (I believe he was just an unfortunate shoemaker who was elected to confront the giant) produces a yellow stone and squeezes it with visible effort, and at last a few drops of water drop to the floor. The giant concedes and leaves the town alone, the 'slayer' returning to a heroes welcome.

The yellow stone is, in fact, the cheese he packed for lunch.

An idiom similar to many others like "struggling to make (both) ends meet" but with a sense of exasperation, or resignation.

Depending on the author's creativity and the context, the expression generally means:

• managing to extract whatever little that is practically possible from a situation/ from something.
• make the most of a situation
• realization of the futility of trying to benefit from a situation or from something

Lisa Romano:

Squeezing Water From a Stone: How to Get More From Existing Capacity and Add More to Your Bottom Line

Brown Advisory Briefings:

Brown Advisory Briefings: Squeezing Water from a Stone

See also:
http://jasongrant.squarespace.com/jason-grant-blog/2010/12/21/you-cannot-squeeze-water-from-a-stone.html
http://www.vahistoryexchange.com/wp-content/uploads/2012/10/Squeezing-Water.pdf
http://briandeutsch.blogspot.in/2007/11/trying-to-squeeze-water-from-stone.html

Exodus chapter 17, verse 6 reads- "I will stand there before you by the rock at Horeb. Strike the rock, and water will come out of it for the people to drink.” So Moses did this in the sight of the elders of Israel.

The idea of getting water from a stone is an unreasonable idea. I think the meaning behind this verse is that it is such a tremendous feat, and yet God could accomplish it with a single strike.

This may not be exactly the meaning you were looking for, but nobody else mentioned it, and I do believe it is supporting evidence of the phrases true meaning.

The idiom 'water from a stone" is correct, meaning a result cannot be produced from a given set of circumstances. Similar, but separate from the idiom, "blood from a turnip."

it means that it is going to take a long time and a lot of hard work