github provides a "Revert" button in it's web interface, which allow us to revert a pull request that was already merged.
This always involves, to the best of my knowledge, creating a new pull request to revert the changes.
Is it possible to replicate this functionality easily using the API? Is it possible to do it without having to create a new Pull Request?
Just to clarify more, the PR is from branch A to branch B - If I undo the changes in branch B using underlying git commands, what will happen to the PR?
There's no API endpoint to do this for you, no. What you need to do is use the SHA of the merged pull request and do a git revert SHA locally followed by a git push to the appropriate branch. That avoid needing to do a new pull request.
If I undo the changes in B using the underlying git commands, what will happen to the PR?
Nothing. It remains merged.