Er hat meine Frage verneint.

English Translation

He answered my question in the negative.

Is this some kind of saying in German? I have never heard anything like this before in American English

yeah, you when you say yes to a question its “bejahen” : “er bejaht die Frage” . And when you say no its “verneinen” : “er verneint die Frage” .

I’m talking about the English translation, it makes no sense to me

Webster knows “answering in the negative” as “with a negative reply”. Rather formal, I would say.