Contact the city building or planning department. Also, file a police report. This is a potentially criminal act. You may have a good claim against the neighbors for damage to your trees. Contact a local attorney for a consultation.
In part this depends on whether parts of your tree were extending into your neighbors yard. If so, the may have the legal right to trim. As for dumping the cuttings into your yard, that seems clearly a trespass and damage to your property.
This is not a legal opinion, and should not be relied upon as such. Contact MARTIN APC at 510-444-7600 with any questions regarding this post.
Neighbor disputes are the absolute worst types of problems - i wish you well and you should seek counsel right away. If you live in a community which is governed by CC&R's, it might be good to contact them and see if they can intervene.