No. I think you mean "Do you know what is the highest mountain in the world?""

I agree with Johnny. You almost had it correct. You just needed to included the word 'know' before the word 'what' for your sentence to make sense. The word 'know' functions as a verb: to know. It helps connects the parts to who you are speaking "Do you" to the rest of the sentence "what is the highest mountain in the world?"

I was thinking about it. But the other native speakers didn't mention it...

It should be "do you know what the highest mountain in the world is?" We don't use inversion in embedded questions.