To fight; not from the Latin miles, a soldier, but from the noun mill. Grinding was anciently performed by pulversing 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.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894