to pare or cut off chips from the surface of (wood) with a knife
to shape or form in this way (something) by doing this
(+ down/away) to reduce, remove, or destroy (something) gradually as if by cutting off bits with a knife
Try to whittle down your expenses
They are whittling away at our rights
[Middle English whittel, alteration of thwitel a paring knife, from Old English thwītan to cut down, whittle]