The fast-paced scenes in Time Piece are edited together in a rhythmic pentameter, with an underlying use of sounds and repetitive beats. The film begins with a young man sitting patiently in a hospital bed. An unidentified doctor enters the room and checks the man's heart rate, which begins to pulse rhythmically. As the rhythm increases, the film begins to follow the man's daily habits such as crossing a busy street, in different clothes and different locations, working in a busy office, working on a conveyor belt, walking through different locations and ending up in a forest where he has the appearance of Tarzan, eating dinner with his wife, walking down the street seeing pogo stick riders, and visiting a strip club while simultaneously maintaining himself in motion. Eventually, the man is imprisoned for shooting the Mona Lisa while intoxicated and dressed as a cowboy and is forced to perform acts of labor like working in the rock pile. The man eventually escapes from prison and begins to frantically run across a long distance with different disguises like a man in a top hat and Tarzan while evading cowboys. The man then jumps off a diving board and soars into the sky where he is subsequently shot down by the world's military powers. He falls from the sky defeated and lands in a muddy puddle in the form of a rustic clock. The clock strikes twelve and the film's events flash quickly on-screen. Back in the hospital room, the doctor covers the man's seemingly lifeless body. The camera then pans up towards the doctor's face, revealing him to be the same man smiling gleefully and winks at the camera.
Unlike most films, Time Piece was not written as a script. Instead, Jim Henson had storyboarded the entire film prior to filming. Between shuffling performances with The Muppets for The Jimmy Dean Show and film commercials, Henson shot the film intermittently from June 1964 to May 1965. Due to this restricted time frame, every shot in the film lasts only one to four seconds. Henson even calculated the amount of frames each shot would contain. Henson solely produced the film's animation sequences, while Muppet designer Don Sahlin was responsible for the film's visual effects shots. Legendary Blue Note Records engineer Rudy Van Gelder recorded the music.
