Cheika responded to last weekend's thrashing by the Brumbies by making six personnel changes and two positional changes.
Mitchell, who has made a slow start to the season, was dropped from the match-day 22 all together, while Lachie Turner and Peter Betham are promoted to form a new starting wing combination.
Wallabies utility Berrick Barnes makes his first appearance of the season, returning from injury at inside centre at the expense of Tom Carter and giving the Waratahs another playmaking option.
Wallabies Test prop Sekope Kepu is the other high-profile star left out, given time off to be with his wife due to the impending birth of their child.
Pat McCutcheon returns to the starting team at No.8, allowing captain Dave Dennis to revert his preferred position on the blindside flank while Mitchell Chapman drops to the bench.
Star signing Israel Folau moves from wing back to fullback, with last weekend's starting debutant Ben Volavola dropped to the reserves.
Turner is elevated from the bench to partner with newcomer Betham as wings.
A stand-out in last season's ITM Cup provincial competition in New Zealand, Betham returns from a trial match ankle injury to take over from Mitchell.
In the other changes to the pack, reserve hooker John Ulugia takes over from the injured Wallaby Tatafu Polota-Nau, while Paddy Ryan gets a start at tight-head.
On the bench, Cheika has opted for a 4-3 forwards-backs split, with Rob Horne included for the first time this year as he returns from a hamstring injury sustained in a pre-season trial.
Teams:
Waratahs:
15 Israel Folau, 14 Lachie Turner, 13 Adam Ashley-Cooper, 12 Berrick
Barnes, 11 Peter Betham, 10 Bernard Foley, 9 Brendan McKibbin, 8 Pat
McCutcheon, 7 Michael Hooper, 6 Dave Dennis, 5 Kane Douglas, 4 Sitaleki
Timani, 3 Paddy Ryan, 2 John Ulugia, 1 Benn Robinson.
Substitutes:
16 Luke Holmes, 17 Jeremy Tilse, 18 Mitchell Chapman, 19 Lopeti Timani,
20 Matt Lucas, 21 Ben Volavola, 22 Rob Horne.
Cheetahs:
5 Hennie Daniller, 14 Willie le Roux, 13 Johann Sadie, 12 Robert
Ebersohn, 11 Raymond Rhule, 10 Johan Goosen, 9 Sarel Pretorius, 8 Philip
van der Walt, 7 Pieter Labuschagne, 6 Frans Viljoen, 5 Francois Uys, 4
Lodewyk de Jager, 3 Lourens Adriaanse, 2 Adriaan Strauss (captain), 1 Trevor
Nyakane.
Substitutes: 16 Ryno Barnes, 17 Coenie Oosthuizen, 18 Landman
Ligtoring, 19 Heinrich Brussow, 20 Piet van Zyl, 21 Riaan Smith, 22 Ryno
Benjamin.