Assuming "sb's" is an abbreviation of "somebody's", it simply means to attack with lethal intent. In the same way, we speak about "going for the jugular", that being a vein in the neck. Wild animals such as lions also almost invariably kill their prey by biting them on the neck, which strangles them to death. Thus, to "go for the neck" means to set about someone with vicious intentions in order to destroy an argument they have put forward, for example.