Brewer's: Whittle Down
To cut away with a knife or whittle; to reduce; to encroach. In Cumberland, underpaid schoolmasters used to be allowed Whittle-gait—i.e. the privilege of knife and fork at the table of those who employ them.
The Americans “whittled down the royal throne;” “whittled out a commonwealth;” “whittle down the forest trees;” “whittle out a railroad;” “whittle down to the thin end of nothing.” (Saxon, hwytel, a large knife.)
“We have whittled down our loss extremely, and will not allow a man more than 350 English slain out of 4,000.” —Walpole.