Having reached 117 for 1 at lunch, the visitors, chasing 324 to win a championship game for only the second time this season, progressed to 189 for 3 at tea.
Mitchell remains unbeaten on 75 despite a difficult afternoon during which he added only 22 runs.
First, he should have been stumped by Chris Read, off Samit Patel, at 139 for 2. Then, he top edged Ben Hilfenhaus over Read’s head. Still, he rode his luck to put Worcestershire in the driving seat with one session remaining.
Tom Fell was first out, after lunch, lbw to Brett Hutton for 58 and Joe Clarke followed at 175 for 3 – bowled by Andy Carter for 33 off 48 balls.
Mitchell and Ben Cox survived the final 33 minutes before the interval and Worcestershire require a further 135 for victory.