A sawmill saws the woodland it stands in whether or not you are there, and goes on doing it while you are logged out. Walk up and press E to empty its yard.
Two things decide whether one is worth building. Where you put it: a mill in deep forest earns its keep, and one on a bare hillside is an expensive shed — it saws the trees around it, and the game reads the real woodland under it. And the yard fills up: it holds forty-eight logs and then stops, so a mill is somewhere you come back to rather than somewhere you forget.
You cannot build one until you know how. A mill is not hard to
build and is very hard to build well — the whole of it is the
axle. There are four old footings and a dry leat in the forest east of the
village, and something split end to end lying in the channel.