You can simply copy the GoMule folder from your old hard drive to your new one. If your stash files are stored somewhere else, then copy those over too.
The GoMule folder has the project files and it references the save files and stash files. It's possible that the file path will be different on your new hard drive (different drive letter or folder hierarchy). You will just need to make sure you reference the new locations for your save and stash files.
For ease of use, I created a separate folder like this:
>GAMES - Diablo II
>all the other game files and folders etc.
>Dump folders etc.
>Folder for each character I play that contains screenshots of drops during questing
>Folder for each area/target that I run that contains screenshots of best drops
* This is the actual game folder
** The folder created when you unzip/install GoMule along with the dump folders, project folders and loose Flavie reports files
*** I create this to keep my stashes by project - all compartmentalised so there is never any cross contamination (prevents HC and SC mixing or twinked and untwinked etc.) This follows the same groupings as my main projects
**** Folder for screenshots (I move them from the Diablo II folder and organise them as I go. I use Bulk Rename Utility on Windows to make this very easy)
Note my stash folder is not in my GoMule folder. This is because I often do 2 different types of backup:
Small Backup = Stashes and Save folder only (Higher frequency)
Full Backup = Whole 'GAME - Diablo II' including screenshots and other notes, all game files, all project and GoMule files etc. (Lower frequency)