American English speaker here. While I would understand what “to auction away” means, I’m not aware of anyone here in California that would say it like that. Usually, I would say “to auction off”, which follows in a long series of other “X off” verbs, like “to bake off” or “to shake off”, all of which usually involve some sort of adversary or competition.

Note that we do use the verb “to give away” but that would mean a gift without compensation, which is definitely not an auction.