To omit George and not use someone or somebody, I think you would probably need to use the passive voice: Henry's eyes were carved out.
To omit George and use an active voice, you could try changing the verb. I'm not entirely sure of the context, but you could say something like: Henry suffered great violence to his eyes, wounds inflicted by a carving knife. Or if it is the case that you're talking about a sculpture, you could say: Henry's eyes came to life, as the carver continued working.
Edit, based on your revised question:
To omit George and not use someone or somebody, I think you would probably need to use the passive voice: Henry's eyes were gouged out.
To omit George and use an active voice, you could try changing the verb. You could say something like: Henry suffered great violence to his eyes, wounds inflicted by a carving knife. Or Henry's eyes suffered horrific wounds inflicted by a knife.
Note that one of the reasons for using the passive voice is "to hide the identity of the agent (doer). The speaker/writer wants to be tactful or evasive." I think yours is an instance of this, so the passive "Henry's eyes were gouged out." may be your better option.