Granny and Tweety go to the beach. While Granny decides to change into her new "bikini bathing suit" (which later turns out to be a one-piece Victorian-style bathing suit), Sylvester who happens to be nearby, who is frustrated with his lack of hunting fish, sees Tweety and decides to have him as his next meal.
After a high tide hits in, Tweety's cage gets stranded by the sea and Sylvester's attempts to eat the bird turn out to be mistaken as his "heroic" attempts to save Tweety by the bird himself and later Granny. Not knowing Sylvester's actual intentions, Granny helps Sylvester to save Tweety with the aid of a diving suit and oxygen tank, which leads the cat to receive all the bad luck (suffocating the cat, shark attack, then overly inflating the diving suit, and later landing the cat in the dog pound) when she joyously runs to reunite with her beloved canary, who has been rowing his cage ashore himself due to him being fed up of waiting to be rescued. Granny appreciates the cat's rescue efforts; she tells the bird, "He certainly deserves a just reward!"
Sandy Claws marks the final time Bea Benaderet would voice Granny; hereafter, Granny would be voiced by June Foray. In addition, after the release of this short, Granny would be overhauled. Her appearance and dress would be updated (starting with "Red Riding Hoodwinked"), and while her cheerful demeanor would be retained (with a few exceptions), her old-fashioned characteristics and mannerisms would be de-emphasized.
It is evident in this cartoon that Granny is unable to relate to the present fads; such as her telling Tweety she's about to try on a new "bikini bathing suit", which turns out to be a one-piece late-19th century/early 20th century Victorian style bathing suit.