I created backup.desktop in /home/pi/Desktop with the code you posted above. I only changed the folder name from /mnt/elements to /home/pi/Test (since I do not have a /mnt/elements, you will need to make sure whichever folder you use exists and is available when running the script - e.g. that the drive is connected to the Pi). It ran just fine when clicked, but did prompt me to execute, execute in terminal, open, or cancel the operation (see below for how to avoid this and the caveats in doing so).
You can also add a custom icon, by adding the following line to your backup.desktop file:
Alternatively, you can create a simple shell script to do this.
using your favorite editor create the shell script:
add the following code:
save the script and exit your editor.
Make the script executable:
chmod 744 open_filemanager.sh
Copy the file to the desktop:
cp ./open_filemanager.sh ~/Desktop
You can now double click the script file from the desktop, but you will be prompted whether to open the file or execute it. Choose execute.
This prompt is a security feature, but if you would like to run the script without prompting you can turn it off (note: since you control the script's contents this isn't really an issue for this script, but this will turn the protection off for all executable scripts).
To turn off the prompt:
Open File Manager
Then open the preferences menu (Edit->Preferences)
On the General tab
click "Don't ask options on launch executable file"
Close the preferences dialog and file Maanger.
You should now be able to double click the icon from the desktop with no prompt.