If you need help following these steps, please submit a REQUEST with "Thunderbird Deleting Attachments" in the Brief Description field.
In the images that follow, the username and account information of an IT employee was used for demonstration purposes. Please replace these entries with your individual information where appropriate.
This documentation shows how to Delete Attachments from Messages.
Regarding attachment deletions.... This is possible but not with the current version of the Zimbra webmail client. You will need to use Thunderbird, if only for this one type of operation.
If you've previously run our copy of Thunderbird from the Novell-delivered applications window, there will be an icon there that says "SAS E-mail." Double-clicking that will launch Thunderbird. If you've not run this before, you will see an icon (maybe two) that says "SAS E-mail Installer." Double-clicking that will automatically configure your Thunderbird profile to use our server. Afterwards, you can click View->Refresh in the Novell window to display the regular "SAS E-Mail" icon to use for launching Thunderbird.
Once in Thunderbird, you can delete attachments by right-clicking on the attachment icon that appears at the bottom of a message containing an attachment. One of the right-click options will say "Delete...." After you've deleted the attachment, the appearance of the attachment icon will change, and the description will now say "Deleted: ." See the screen shot below to see how this will look in Zimbra.
I recommend performing the attachment deletion from the preview pane. That is, rather than double clicking a message to view it in its own window, just click on the message *once* so that you can see a preview of the message and its attachment icon in the lower right pane. Then right-click on the attachment icon that's visible in there and choose the Delete... function. For some reason, using this function in the preview pane seems to cause less confusion.
Note also that Thunderbird has the ability to let you sort messages by size. (See here for instructions). Taking advantage of this feature would help you find the messages with the largest attachments first, so you'd get the most bang for your buck.