Avodah Zarah, Chapter Three, Mishnah Ten
Our mishnah asks how does one annul an asherah in order to make it permitted for Jews to use.
1) How does one annul [an asherah]?
a) If [a pagan] pruned or trimmed it, removing from it a stick or twig or even a leaf, behold it is annulled.
2) If he smoothed it out for its own sake, it is prohibited;
a) but if not for its own sake, it is permitted.
As we will learn in the next chapter of mishnah, a pagan can annul his idol by stopping to treat it as such. If he does so, what was formerly an idol reverts to being a normal object and a Jew may use it. Our mishnah teaches that removing a piece of an asherah tree is a sign that it is no longer being worshipped. Evidently the asherah was not used by the pagan for anything but idol worship. If the pagan does make even the most minimal use of the tree, such as using its leaf, it loses its status as an asherah. The only exception to this case is if he removes something from the tree for its own sake. In other words, if he smoothed the tree to make it look better, it is still an asherah and it is still forbidden. If he did so in order to get a branch, he has annulled its status as an asherah and it is permitted.