"He left without say a word" is not English. Is it pidgin? Why do 15.22% of poll-takers approve of it?
He left without saying a word, is simple and correct english language.
In this way we use "saying' because after without we should put Gerund.
I am greatly surprised just how it could be "say a word" , ....must have been their eminence , I suppose.
I do believe that its answer is "saying".