the space covered by the stroke of a scythe or the cut of a mowing machine.

the piece or strip so cut.

a line or ridge of grass, grain, or the like, cut and thrown together by a scythe or mowing machine.

a strip, belt, or long and relatively narrow extent of anything. ?

cut a swath

to make a pretentious display; attract notice

The new doctor cut a swath in the small community.