You cannot extract what isn’t there to begin with.
This Old English proverb is first recorded in a collection of letters entitled Winter Evenings, by Vicesimus Knox, 1788:

They must have had abilities inherent in them or they could not have been excited, according to that common observation, that it is impossible to get blood out of a stone.

You can’t get blood out of a stoneThere is, however, good reason to believe that phrases of the form ‘you cannot get blood out of a [inanimate object of your choice]’ originated in Italian and were later translated into English.

In the 1640s to 1660s the Italian writer Giovanni Torriano wrote several books to aid Italian/English translation. They had subtitles like “Select Italian proverbs the most significant, very usefull for travellers, and such as desire that language: the same newly made to speak English…”

In Torriano’s Piazza Universale di Proverbi Italiani, 1662, we find:

There’s no getting of bloud out of that wall.

In his Second Alphabet of Proverbial Phrases, 1662, Torriano used the variant of this proverb that is best known in the USA, that is ‘get blood out of a turnip’:

To go about to fetch bloud out of a turnip, viz. to attempt impossibilities.