Both stars were nominated for Oscars on Monday.
Kaluuya earned a Best Supporting Actor nod for Judas and the Black Messiah and Mulligan is up for Best Actress for Promising Young Woman.
Kaluuya will host the April 3 episode of SNL when St. Vincent will provide the night's musical entertainment.
Mulligan is set to appear in the April 10 edition of the sketch-comedy show. Kid Cudi will be the musical guest.