If I made some contributions to a repository on GitHub and then decided to delete the source code that I contributed, are other users of the repository still allowed to use that particular source code? This particular repository is under the GNU license and I pushed some code to that repository that I shouldn't have and I'm going to permanently delete it. However, some other contributors to the same repository may have clones of it on their local machine and may reupload my code back to the repository. Are they allowed to do this or can I stop them from doing it as I was the one who wrote the source code?
You are not allowed to prevent this.
You made the software available to them under the terms of the GNU GPL, and those are irrevocable. You are completely free to stop publishing it on those terms, but people who already have it under them may continue to use it under those terms, which include the freedom to copy it (to the original git repository, if that is technically possible, or to any other place) so long as they also do it under GPL.
However, you say that you "pushed some code to that repository that I shouldn't have", but you don't explain why. If you never controlled the rights to the code you pushed, for example because you wrote it for an employer who retained the rights, you were not lawfully able to do what you did: you are not taking away rights you previously gave, you are informing everyone that you gave away something you never had any right to give. No project wants to use rights-contaminated code, so you can go back to the project and explain in painful detail exactly what the issue is, and what code has to be excised. It will be embarrassing and public, and should serve as a useful reminder to you never to do that again.