is the phrase correct...?

In what context might you want to say such a thing?

AnonymousIs it possible to use such a phrase "Because of us to drive fast"?

I can't think of any way to use that phrase in a sentence, so I'd say no.

It seems that you're aiming at something like one of these:

... because we were driving (too) fast.
... because we drive (too) fast.
... because we drove (too) fast.
... drove (too)

We really had to get there in a hurry. Did he think it necessary because of us to drive fast?

You can find a way to use practically any string of words. Your question is pointless. Please provide a complete sentence using the phrase the way you imagine it might be used.