Publish the sheet separately. Save the URL for that sheet.
It will have a string like this at the end of the URL: "?:iid=1"
Delete that part.
Tack on ".pdf" to the end of the string.
Tableau Server will create your sheet as a PDF. You don't have a lot of control over it, as far as I can tell, such as telling it to do landscape instead of portrait, or size, etc.
Give that a try. See if it works for you.
Take a look in the Chrome developer console or use Fiddlr to inspect your traffic once you hit 'Download'. You'll see a post request like https://public.tableau.com/vizql/w/RegionalSampleWorkbook/v/Obesity/sessions/1B831EA6789F466C8066926276660183-0:1/commands/tabsrv/pdf-export-server
You could mimic that and put a button in there which runs that. It's probably not supported though.
Thanks. Unfortunately it gives me a resource not found. Appreciate the idea.
What gives you a Resource not found? That link above? If so, that is expected, that link won't work as it's just an example.