Lady and the Tramp meet Mr. Busy when trying to get Lady's muzzle off. A tree chewed down by Mr. Busy nearly falls on them, and the Tramp barely warns Lady in time to get out of the way. They see him chewing down branches and sections of the tree in order to finish his dam. This gives the Tramp an idea on how to remove Lady's muzzle. Mr. Busy struggles to push the log that he chewed over to the spillway and originally refuses to listen to the Tramp, saying that he is busy, but the Tramp then shouts in Mr. Busy's ear that he needs a log puller. This gets Mr. Busy's attention. The Tramp takes on the role of a salesman and convinces Mr. Busy to bite the muzzle off, much to Lady's relief. Mr. Busy starts pulling the log using the muzzle, which he believes to be a log puller. It works all too well and Mr. Busy is flung through the air, still attached to the log, and eventually lands in the water. The log floats over and completes the dam, much to Mr. Busy's delight. He isn't seen throughout the rest of the film.
Mr. Busy makes a cameo appearance along with the other forest animals (including two red robin birds, three dark blue possums, an eagle, a bear, a raccoon, and a moose), all of which were not pleased with Donald's littering and are seen holding a sign that says, "Keep your Country Beautiful".
In the Disney+ exclusive film, Mr. Busy himself does not make a physical appearance, though a beaver statue taking the role of the aforementioned character can be seen in the park scene. In it, Lady and Tramp go to the park to get the muzzle off her mouth where Tramp helps Lady remove her muzzle by using a beaver statue to pull it off.
Mr. Busy's model would later be used for Gopher, a character from the Winnie the Pooh franchise. Coincidentally, both characters speak with the same accent. Some of the recycled animation of the beaver was also used for Gopher in Winnie the Pooh and the Honey Tree in one scene.