The expression “to cut a big swath” was slang, back in the 1840’s.
It alluded to the wide sweep of grass mowed by a scythe; hence, to the flourish made by a pompous person swaggering down the walk.
In fact, the first literary use of this American slang was precisely that.
It was in High Life in New York (1843), by Ann Stephens: “Gracious me! how he was strutting up the side-walk, didn’t he cut a swath!”
The popular creator of the fictional character, Sam Slick, undoubtedly helped perpetuate the phrase.
In Nature and Human Nature (1855), that is, Thomas C. Haliburton had the lines, “The Miss As cut a tall swathe, I tell you, for they say they are descended from a governor of Nova Scotia, and that their relaticins in England are some punkins too.”