A person can express their dislike or disapproval in several ways without resorting to physically attacking someone. Here are some synonymous phrases for "throwing stones at":
1. Criticizing harshly
2. Making scathing remarks
3. Hurling insults
4. Casting aspersions
5. Engaging in character assassination
6. Slinging mud
7. Picking apart
8. Mocking
9. Belittling
10. Deriding.