You cannot drag and drop diagrams between Gliffy Online and Google Drive. You may receive an error if you attempt to do so.
If you have a diagram stored in Gliffy Online and want a copy stored in Drive (or vice versa), start by opening up your existing diagram.
Go to File->Save As and select the location you want to save a copy to. To save a copy in Drive, select Google Drive.
Your Google Drive folders should appear and will let you select what folder and what name you want to save it as. Once you have selected the folder location and named the diagram, click Save.
Your diagram should now show a copy in Google Drive. Please note, this saves a new copy and any changes to the original would not affect the new version. If you only want one copy, delete the previous diagram from either Gliffy Online or Drive.
This procedure also works in reverse. If you would like to take a diagram from Google Drive and make a copy in Gliffy Online, go to File->Save As and select the Gliffy option.