Oracle on Oath of Druids:
At the beginning of each player's upkeep, that player chooses target player who controls more creatures than he or she does and is his or her opponent. The first player may reveal cards from his or her library until he or she reveals a creature card. If he or she does, that player puts that card onto the battlefield and puts all other cards revealed this way into his or her graveyard.
Oracle on Gaea's Blessing:
Target player shuffles up to three target cards from his or her graveyard into his or her library.
Draw a card.
When Gaea's Blessing is put into your graveyard from your library, shuffle your graveyard into your library.
Basically, Blessing doesn't trigger until after the Oathed creature hits the board and all the cards are then put in the Graveyard. Once Blessing physically hits the graveyard, the trigger goes on the stack. With Blessing's trigger on the stack, you can Extirpate any of the cards in the Graveyard, including the Blessing.
You are getting confused thinking that Blessing is a replacement effect, when it is actually a triggered effect. A card like Leyline of the Void is a replacement effect:
If Leyline of the Void is in your opening hand, you may begin the game with it on the battlefield.
If a card would be put into an opponent's graveyard from anywhere, exile it instead.
With Leyline in play, cards never actually touch they graveyard.
The Blessing has to touch the graveyard to trigger, which means that it is physically in the graveyard for small amount of time, but both players get priority when the trigger goes on the stack.
