E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To fight; not from the Latin mils, a soldier, but from the noun mill. Grinding was anciently performed by pulverising with a stone or pounding with the hand. To mill is to beat with the fist, as persons used to beat corn with a stone.
The word is Gaelic, in which there are numerous derivatives, meaning to ravage, destroy, etc.