Print All Attachments

Make a folder action to do it.

Create a folder that you want to save the attachments to.
Open Automator and make a workflow with just the Print Finder Items action in it--Click on Finder from the Library list, then drag the Print Finder Items action to the right pane of Automator.
Select the appropriate printer in the "Print to" pop-up menu.
Select "Save as Plug-in..." from the File menu.
Choose "Folder Actions" from the "Plug-in for" pop-up menu.
Choose the folder you created at the beginning as the folder for the action to be attached.
Click Save.

Now, when you Save Attachments from Mail, save them in the folder you created and the folder action will run and print the files. You could even use the Keyboard and Mouse System Preference to make a keyboard shortcut for the Save Attachments command.

If you want to delete them immediately after printing, just add the "Move to Trash" action after the Print action.--This just deletes the attachments you saved, not the ones in the message.

Hello Dean.

Not sure what makes you think this is simple thing for Mail to do, since each attachment might require a different application to print it.

What you can do is select those messages, do File > Save Attachments, then select the corresponding files in the Finder, and do File > Print on them.