of (prep.) [⇐] Old English of, unstressed form of æf (prep., adv.) "away, away from,"
from Proto-Germanic *af, [...], from PIE *apo- "off, away" (see apo-). Primary sense in Old English still was "away," but shifted in Middle English with use of the word to translate Latin de, ex, and especially Old French de, which had come to be the substitute for the genitive case.
After my long tiresome enervated search, Google discovered a book that addresses my question briefly: pp 209-212, 235-236 of The Semantics of English Prepositions; Spatial Scenes, Embodied Meaning, and Cognition (Reprint ed, 2007) by Andrea Tyler, Vyvyan Evans. It quotes the OED's etymology of of that confirms the above etymons' influence on the Semantic Field of of.
But how did 'off, away, away from' change semantically into the more figurative meanings? I ask about the big picture and semantic field of of just like how this explanation explains the underlying meaning of ‘tally’.