You can use Git and the API to back up your repository.

You can download and back up your repositories manually:

When you clone a repository or wiki, only Git data, such as project files and commit history, is downloaded. You can use our API to export other elements of your GitHub Enterprise repository to your local machine:

Once you have a local version of all the content you want to back up, you can create a zip archive and copy it to an external hard drive and/or upload it to a cloud-based backup service such as Google Drive or Dropbox.