mill (n.1) Look up mill at Dictionary.com
"building fitted to grind grain," Old English mylen "a mill" (10c.), an early Germanic borrowing from Late Latin molina, molinum "mill" (source of French moulin, Spanish molino), originally fem. and neuter of molinus "pertaining to a mill," from Latin mola "mill, millstone," related to molere "to grind," from PIE *mel- (1) "soft," with derivatives referring to ground material and tools for grinding (source also of Greek myle "mill;" see mallet).

Also from Late Latin molina, directly or indirectly, are German Mühle, Old Saxon mulin, Old Norse mylna, Danish mølle, Old Church Slavonic mulinu. Broader sense of "grinding machine" is attested from 1550s. Other types of manufacturing machines driven by wind or water, whether for grinding or not, began to be called mills by early 15c. Sense of "building fitted with industrial machinery" is from c.1500.
mill (n.2) Look up mill at Dictionary.com
"one-tenth cent," 1786, an original U.S. currency unit but now used only for tax calculation purposes, shortening of Latin millesimum "one-thousandth," from mille "a thousand" (see million). Formed on the analogy of cent, which is short for Latin centesimus "one hundredth" (of a dollar).
mill (v.2) Look up mill at Dictionary.com
"to keep moving round and round in a mass," 1874 (implied in milling), originally of cattle, from mill (n.1) on resemblance to the action of a mill wheel. Related: Milled.
mill (v.1) Look up mill at Dictionary.com
"to grind," 1550s, from mill (n.1). Related: milled; milling.