Sitting at Olive's cafe, Popeye and Bluto watch her as she sings "I Want A Clean Shaven Man" while going about her business. Not only is Bluto bearded but Popeye shows abundant stubble on his face. The two get an idea and run off to Wimpy's Barber Shop, where they enter, demanding service, until they notice the "BARBER OUT GETTING A SHAVE" sign. They decide to give each other a shave and haircut, with Popeye leaving Bluto with an elegant mustache and hairdo. The latter, however, treats his sailor rival to a broken razor and scalding towel, leaving him with a messy appearance. When Popeye notices, he is given a beating and dragged away for Olive to make her choice. By eating spinach, not only is Popeye made stronger but also perfectly groomed, turning the tables and dragging the now messy Bluto for Olive to choose. However, they see her going on a date with the bearded George W. Geezil, and end the cartoon kicking each other.
Shaving Muggs is a color remake of 1936's A Clean Shaven Man, released by Famous Studios in 1953 as the 200th Popeye cartoon.
Bluto and a stubble-faced Popeye are Navy sailors arriving at the dock and wanting to take Olive Oyl out for a date. Their struggle at her doorstep is cut short when she says either should have a shave and a haircut if they are to go out with her. They dash off to Wimpy's Barber Shop, but it is closed, with a sign saying "OUT TO LUNCH" hanging on the door. Bluto suggests they shave each other and they enter anyway. Popeye does a thorough job shaving off his fellow's rough beard and bringing down the last of his rebel hairs, but Bluto is more devious. Starting with a scalding towel, he then uses cement for shaving cream and gunpowder all over his companion's head. After the resulting barbershop-leveling explosion, Popeye sees his spinach can fall nearby and, although his mouth is encased in cement, he is able to suck the vegetable with his protruding pipe. He is now able to mess up his earlier work on Bluto, but then both notice Olive passing by, on a date with a ship's captain whose long beard she finds "utterly distinguished". The two rivals then proceed to kick each other.