It's not possible to download a copy of your dashboard as a PDF, but there's a wealth of alternatives available to you if you need to share a PDF snapshot of a dashboard:
If you're a Chrome user, you can install an add-on such as Full Page Screen Capture to take a screenshot of the entire dashboard and save it as a PDF.
Similar to the above, if you're a Firefox user, you can install an add-on such as Fireshot for the same purpose.
Regardless of your browser or OS, a solution like CloudApp will allow you to snapshot a dashboard in a way that's ready to be shared as an image.
If the use of PDFs isn't essential, one of the best ways to share snapshots of your dashboards is via email.