As we read through the poem, the soft whispering of all the S sounds becomes almost hypnotic. Just count the S's at work in the first two lines:
There was never a sound beside the wood but one,
And that was my long scythe whispering to the ground.
It isn't meant to be particularly soothing, though—more like the hypnosis of Willie Wonka's psychedelic boat ride in the original movie. It's meant to lull you into an understanding rather than a nice nap, which is precisely the effect that the hypnotic sound of the scythe seems to have on the speaker. The words mimic the sound of the scythe cutting through the grass and then cutting through the air on the backswing.
As well, the wooshing of the W sounds is very much like a long, sharp blade moving swiftly backward through the air. Along with the S's, the these W sounds continue through every line of the poem, creating the impression that we are right there with the narrator (though probably sitting in a shady spot with a nice cold glass of lemonade and letting him do all the dirty work).
For the record, this isn't just a one-time technique either. Frost had a whole "sound of sense" or "sentence sound" theory for his writing. His goal was to "make music" with his words. He believed in this so much that he often expressed frustration in his letters to colleagues about other poets who weren't paying as much attention to the phenomena of sound in their poetry as he was.