The song epitomizes Primus's musical eccentricities, whereby the group's signature funk metal stylings are comically inflected with a sound vaguely reminiscent of bluegrass and southern rock. During the song's guitar solos, Larry LaLonde's playing shifts from almost "noise" guitar in the first solo to a somewhat country-sounding technique and banjo-style finger-picking on the second (inspired by The Grateful Dead late singer/guitarist Jerry Garcia). The song's lyrics constitute an absurd, rambling tale about a woman named Wynona and her "beaver". They combine an on-the-surface crude sexual double entendre in "beaver" with the more purely nonsensical silliness typical of the band (e.g., strange references to baboons, Taco Bell, carnies, and porcupines).
The band also filmed a music video for "Wynona's Big Brown Beaver", centered on the band dressed as comical-looking cowboys in costumes made of foam rubber. The costumes bore a strong resemblance to those used in a popular Duracell advertising campaign at the time which featured a family of battery-powered, toy-like people (the Puttermans). In an interview, bandleader Les Claypool revealed the suits were intended to resemble "cheap plastic cowboy action figures". The video jumps between shots of the band playing in a barn and of the band engaged in parodies of cowboy activities such as shooting bottles, riding toy horses, and playing poker among other things. The video also features some airbrushed drawings done by Claypool. The video's live action sequences were filmed at Claypool's home, known as Rancho Relaxo. The video marks the second video appearance of Les' red Fender Jazz bass.
Because the band's cowboy suits were so cumbersome, they played along to the track slowed down significantly to more easily coordinate their actions to the music; plus, this gave the illusion of the band moving rather quirky and fast when played back in regular form. In the video, Tim Alexander's bass drum reads "Buck Naked and the Bare Bottom Boys". This was meant as a tribute to Phillip Bury, who went under the name Buck. He was a close friend to the band, who had died in 1992. He was in the aforementioned Buck Naked and the Bare Bottom Boys. The video appeared on Primus' Tales from the Punchbowl [CD-ROM] album as well as the 2003 EP/DVD release Animals Should Not Try to Act Like People, along with an in-depth making-of feature.
Many incorrectly believed "Wynona" was about actress Winona Ryder. Claypool has stated several times that the song was not written about anyone in particular, especially Ryder, and was surprised he wasn't asked about country singer Wynonna Judd instead, considering the song's country music influence and the name being pronounced and spelled with a "y" which was closer to Judd's name.  While this placated Ryder, her then boyfriend Soul Asylum vocalist David Pirner took offense and renamed one of his songs "Les Claypool's A Big Fucking Asshole" in concert.
One of the song's lyrics was edited in the music video. The original line, "But the beaver was quick and grabbed him by the kiwis, and he ain't pissed for a week (and a half!)" was replaced by "...and he egg-pressed for a week...". An alternative version also removes the line "candied up his nose" (which refers to cocaine) and the word "smell", replacing them with random sound effects.