Here we'll talk about how a non-Jew could nullify an idol. The Mishnah says: How does a non-Jew nullify an idol and make it permissible to benefit from it? He cut off the tip of the ear, the tip of the nose, or the tip of the finger, even though he left the rest of the idol's body intact. Or let's say he took a metal hammer and smashed the face of the idol. Even though nothing was removed from it, its entire appearance—the features of its face—was now off. In these cases, he nullified it because he showed that he no longer considered it to be a god. Therefore, at that point in time, you would be permitted to benefit from it.
But if he spit on it or in front of it, urinated on it, dragged it through the mud, or threw excrement at it, he has not nullified it. Even though the actions he's doing here show a lack of belief in the idol, it's very possible that this is only a temporary lack of belief. Maybe the idol didn't answer him in a tefillah, a prayer that he wanted. Maybe he was angry at the idol, so he did something like that. But maybe when his emotions change, he'll be back to worshipping that same idol. Therefore, those actions wouldn't nullify the idol. Only actions that cause permanent damage are considered nullification.
If he sold the idol or gave it to somebody as security for a loan, he has nullified it by doing so. He shows that he doesn't have any belief in the idol by giving it away for money. If he's using it for something so mundane as giving it away for money—giving away his idol for that type of purpose—obviously he doesn't believe in it anymore. Therefore, you're allowed to benefit from it.
VehaChachamim omrim lo bitel. VehaChachamim say no. He hasn't nullified it. He gave it away only because he temporarily needs the money, and he thinks that the idol is still going to be worshipped. In other words, he's giving it to somebody because he thinks the idol has value as a religious object and that it could still work. So he's giving it to somebody, and at least that other person will use it. Therefore, VehaChachamim say: VehaChachamim lo bitel. He has not nullified it.