GitHub Pull Request errors
You can add a second commit and push to the same branch, which is what I'd generally do. The PR will be updated with additional commits to the PR's branch. 

git add --patch
git commit
git push REMOTENAME BRANCHNAME


If your branch hasn't been merged (and you're not concerned about others having worked on the same branch), you can also amend your commit and then force-push. But this is more likely to cause grief IMO. 

git add --patch
git commit --amend
git push -f REMOTENAME BRANCHNAME


If you really regret a PR, you can delete the remote branch and start over. This will probably destroy the PR, but you can make as many branches and pull requests as you like.

A colon before the branch name will push "nothing" to that branch, deleting it.

git push REMOTENAME :BRANCHNAME