My essay was graded 0% because of late submission on Turnitin. I have a new deadline to retrieve now, but what will happen if I submit the same paper again? Did my essay go to waste?

That’s a fantastic question for your instructor, and a terrible question for anyone else.

Only your instructor can tell you whether they will accept the the paper that you tried to submit late, or if they will insist that you write a completely new paper.

(And even if they insist on a new paper, the first essay didn’t “go to waste.” The point of asking you to write essays is to give you practice writing. Your first essay gave your that practice even if you never get credit for it. In the long run, the writing practice is far more important than the points.)