"ponder, turn over in one's mind," 1873, perhaps from a figurative use of mull (v.) "grind to powder" (which survived into 19c. in dialect), from Middle English mullyn, mollen "grind to powder, soften by pulverizing," also "to fondle or pet" (late 14c.), from Old French moillier and directly from Medieval Latin molliare,mulliare, from Latin molere "to grind," from PIE root *mele- "to crush, grind."
Of uncertain connection to the mull (v.) defined in Webster's (1879) as "to work steadily without accomplishing much," and the earlier identical word in athletics meaning "to botch, muff" (1862). Related: Mulled; mulling.