Whether the dogs must be euthanized is a matter of state and local law. I do not practice in GA and cannot comment on that issue.
I can suggest that, if you have not already done so, the attack be reported to the police and animal control at once. Also, document all your damages from the killing for use in a demand letter and, almost certainly, a small claims action against the neighbors.
Note that there will be no pain and suffering, loss of consortium, etc.; only the fair market value of your dog.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
This can only be done through your local Superior Court. Start by filing a police report.
James L. Yeargan, Jr. is licensed to practice law in the State of Georgia. All information given is based only on Georgia law, and is not directly applicable to any other jurisdictions, states, or districts. Any answer given assumes the person who asked the question holds a Georgia Drivers License, and this license is not a commercial drivers license (CDL). This response, or any response, is not legal advice. This response, or any response, does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information. Any state specific concerns should be directed to an attorney who is licensed to practice law in that respective state.