Strange, I have never seen that problem on any Mac, mini or otherwise. Apple's do NOT add advertisements to any emails at all, so I think you are either exaggerating or you have some weird email senders.
Are you using Apple Mail or getting it on your browser? Perhaps you've allowed a tool bar or two to be installed on your browser? If so, that is not Apple, that was YOU OKing a download you should not have.
You usually get these by installing a FLASH player from a non-official source.
Check this source for ways to remove it:
LOL