Answer:
A crafty use of long pieces of wool to make a scarf.
Up on high I wave away but not a word can I say.
The more you take, the more you leave behind. What are they?
Rotten trees and Jack-O-Lanterns have this characteristic in common.
My second is performed by my first, and it is thought a thief by the marks of my whole might be caught.
Though not a plant, has leaves. Though not a beast, has spine. Though many wouldn't need this thing, It's more valuable than wine.