Under Mourinho's predecessor, Manuel Pellegrini, Real were humiliated 4-0 by Alcorcon, another third-tier side, in the same fixture last season and failed to turn the tie around at the Bernabeu to slump to an astonishing 4-1 aggregate loss.
Mourinho said after Real's 6-1 La Liga thrashing of Racing Santander on Saturday he would give Mesut Ozil, Xabi Alonso and Ricardo Carvalho a few days off but planned to field the in-form Cristiano Ronaldo, who has netted eight goals in his last three league outings, and out-of-favour France striker Karim Benzema.
"If last year's situation (at Alcorcon) repeats itself, I will cross those who play off my list because they will be dead to me," the flamboyant Mourinho told a news conference, invoking the main character in the hit U.S. TV series The Sopranos.
"Benzema will start and so will Ronaldo. It is a very important game to me," he added.
Real have not won the King's Cup since 1993, while arch rivals Barcelona's last triumph came in 2009 when they won an unprecedented treble of Champions League and domestic league and Cup.
Pep Guardiola's side have a short hop by helicopter to north Africa to the autonomous Spanish city of Ceuta where they take on the local side in their 6,500-capacity Alfonso Murube stadium on Tuesday.
Guardiola left World Player of the Year Lionel Messi and most of his Spanish World Cup winners, including goalkeeper Victor Valdes, defender Gerard Pique, midfielder Andres Iniesta and striker David Villa, out of his 16-man squad for the trip, instead calling up several players from the youth squad.
Spain midfielder Xavi, who missed Saturday's 2-0 La Liga win at Real Zaragoza, is still shaking off an Achilles problem and central defender Gabriel Milito is unlikely to have recovered in time from a thigh strain.
Guardiola told a news conference on Monday he needed players with fresh legs.
"Those who are coming with us know the lower divisions and how hard it is to play at those stadiums," he added.
In other first legs, holders Sevilla face Real Union (third tier) on Wednesday.
There are two ties featuring clubs from the top flight as Hercules take on Malaga and Real Mallorca play Sporting Gijon, both on Wednesday.
The return legs are in the second week of November.
