At close, Smith was on 229 and Mitchell on 181 even as England had fallen 146 runs behind after conceding 346 runs for just one wicket.
England assistant coach Paul Farbrace said the weaknesses in the English attack, particularly in foreign conditions, were being cruelly exposed.
Yes, getting Smith out is easier said than done. "There is nothing that has surprised us".
Although the Somerset seamer could not add to his two first-innings wickets, the fact he was out there at all on the 13th day of a scheduled 25 showed his commitment to the Ashes cause after early-morning scans revealed a crack in the ribs he damaged attempting to take a return catch the previous evening.
However, he wouldn't concede the Ashes defence was over.
Smith's both Test double centuries have come against the same opponents, having hammered England for 215 at Lord's in the 2015 Ashes series. Heavy rain is forecast for the fourth day, but is not predicted to arrive until late in the afternoon, reducing the chances of a draw.
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Steve Smith's Test average also crossed 61 during his knock - a figure second only to Sir Donald Bradman (99.94) among batsmen with more than 5000 runs in Test cricket.
Mitchell, meanwhile, got to his maiden Test century on his home ground.
Farbrace conceded the English were nearly powerless to stop Smith in his current form. "When it comes to flatter pitches, we don't have that express pace".
Instead it seems like Australia will bat on for as long as they like, and an exhausted England will probably fall apart as soon as their turn comes around, the pitch flips once more from genteel promenade to lightning-infused viper pit.
Resuming on 92, Smith reached his 22nd Test century off 138 balls, his quickest in terms of balls faced.