The earliest cutaway set that I could find was designed by innovative French director Maurice Tourneur for the crime drama The Hand of Peril (1916).
Charley Chase wrote and directed Ship Ahoy (1919), which used the cutaway set to show comedian Billy West being chased around a ship by a sea captain's evil henchmen.
Buster Keaton staged his own comic chase in a cutaway set for The High Sign (1921).
Busby Berkeley came up with this cutaway hotel set for a musical number of Footlight Parade (1933) called "Honeymoon Hotel."
The elaborate boarding house set that Jerry Lewis created for The Ladies Man (1961), which was used extensively throughout the film, left a lasting impression on viewers.
Jean-Luc Godard, a French filmmaker who admired Lewis' work, designed an office set similar to Lewis' boarding house set for Tout va bien (1972).
Another homage to Lewis' set turned up in Absolute Beginners (1986). It is also a boarding house.
Jameson pointed out the similarities of Lewis' boarding house and the restaurant Le Hollandais from Peter Greenaway's The Cook, the Thief, His Wife and Her Lover (1989). Jameson wrote, "Greenaway is cutting between different sets here, but his montage achieves a somewhat similar effect." Both the restaurant and the boarding house are buildings with many different candy-colored compartments.
A series of compartments with flamboyantly diverse designs appear in the 1998 music video for The Smashing Pumpkins' "Ava Adore." Jameson wrote, "Obviously, the further we get from 1961, the less certain it is that any particular film is directly influenced by The Ladies Man. Nonetheless, the video that Dom and Nic directed for Smashing Pumpkins’s 'Ava Adore' must count as some kind of descendant."
Martin Scorsese's Gangs of New York (2002) features a nightmarish version of Lewis' boarding house. Methodist missionaries have converted an abandoned brewery into a warren of dark, cramped apartments to house the poor.
Finally, we have another cutaway ship set from The Life Aquatic with Steve Zissou (2004).