There may be other ways by now but one way that should work in many Calibre versions is to type a year of 0000.
I know as of a couple of releases ago there is also the ability on the bulk metadata dialog to clear the published date (the icon to the right of the date).
I would still love a setting/tweak to make the default behaviour of Calibre to leave it empty rather than putting todays date in it. At least now we can in bulk blank it out but imho we shouldn't "need to". There's been an open ticket for it for a while... I've tried a few times to find the right place in the code but it has eluded me. Commenting out lines which seemed obvious didn't achieve the goal, leaving me wondering if it was a database default field or something.