No. In Washington State, a DUI conviction cannot be removed from one's criminal record (except by direct pardon from the Governor).
If the latest charge was amended to something other than DUI, there has been no convictions for anything since and no pending charges, you could petition the court to remove the most recent charge. This is discretionary and the judge will likely deny your request because of the prior DUI.
You may be able to vacate your second conviction, but only after at least ten years has lapsed with no subsequent criminal convictions. Since your DUI convictions could potentially be used against you in a futurevehicular homicide/assault case, courts are unlikely to vacate it any earlier.