How do I print an email from Mail.app without mail headers?
It's a workaround. But when you select the text you want to print. Right click and select under services the option 'New Text Edit window containing text'

This opens the selected text in a new text edit file.. From there you can print.

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How to turn it on

If this option is  not visible.. you can turn it on at

System Preferences -> Keyboard -> Shortcuts -> Services

Scroll to the text section and turn on 'New Text Edit window containing text'

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Automator Action

I've made an automations.. 

selected text -> right click -> services -> print email

Instructions and download are here...