Unless there has been some special ruling that I'm unaware of...(*1)
When Grindstone is activated and the target player's library contains nothing except two Serra Avatars(*2), the game enters an uncontrolled loop and ends in a draw.
Here's why:
We'll assume that there is nothing in play that can interfere with the process, such as another effect that replaces cards going to the graveyard.
When Grindstone's ability resolves, you put the top 2 cards of your opponent's library into the graveyard. If those cards are
both Serra Avatar, the event "Put these two cards into their owner's graveyard," becomes "shuffle these two cards into their owner's library."(*3)
So when you reach the final part of Grindstone's instructions ("If both cards share a color...") you must repeat the process. Every time, you will be shuffling the two Serra Avatar cards back into the library, and repeating the process. Since no player will ever gain priority, no one can stop it, and the game ends in a draw.
Notes:
*1 - It's remotely possible that it's been rules that the cards must actually go to the graveyard for the second instruction to apply. You can make a very good case for this. Since the library is a "secret info" zone, the colors of the cards is unknown to Grindstone until they go to the graveyard (a "public info" zone). Although the Serra Avatars are revealed as part of their replacement effect, you could say that since Grindstone will be looking to see what color the cards it put into the graveyard are, it doesn't find them there and won't know that they shared a color.
This is a bit shaky, but it could fall under the same reasoning that dictates that Memory Lapse must actually counter it's target in order to put it on top of it's owner's library.
Any confirmation/denial of this would be appreciated, although I don't expect it to keep me up at night.
*2 - The same result can be achieved with exactly two Legacy Weapons in the target player's library and Celestial Dawn under that player's control.
*3 - This is simplified, but I'm not even sure how you'd word the actual events, and the result is exactly the same anyhow. So, nitpickers begone!
[Corrected an error where CT put "graveyard" instead of "library." --Zadok001]