The smaller site will have to do what Voat is currently doing and restrict registrations and access for a while. Ultimately the fact that big players can shove smaller players off line is weakness of IPv4 address exhaustion and designing platforms on a strict centralized client-server model, not a model of suppressing violence-inducing speech.
> I don't have the resources or people to deal with that. Should I be taken down for something I can't control?
Yes, because you can put a banner on your page "Hey users, we can only support X users for required moderation of violent content with our current resources. Will you give us more money to support X+Y users?"