Bugs wanders onto the screen munching his obligatory carrot and absent-mindedly begins reading the title card, grossly mispronouncing all of the credits, such as for "Avery" rather than the correct name When he finally gets to the turtle itself, he becomes outraged, tears apart the title card, and rushes to Cecil Turtle's house. He then bets the little, sleepy-eyed turtle ten dollars that he can beat him in a race.
Cecil accepts Bugs' bet and quickly (for him, anyway) calls up Chester Turtle and eight other cousins, all of whom look and sound like Cecil (some have deeper voices, some have higher voices). After talking to Chester about the bet, he tells him to call the other cousins and tell them to be ready when he comes to their position, and to "give him all the works". Fade to black (he possibly says goodbye and hangs up). The race begins several days later, and as Bugs runs relentlessly toward the finish line, Cecil and his relatives take turns showing up at just the right moment to baffle the bunny. In the end, Bugs is convinced he has won, only to see Cecil (or one of his kin) across the finish demanding the money. Bugs suggests that he has been tricked, and all ten turtles approach and reply, "It's a possibility!" And they all kiss Bugs. Mel Blanc supplies Cecil's drowsy drawl, which is like a slowed-down version of Blanc's later characterization of Barney Rubble.
"Tortoise Beats Hare" is, of course, a take off of the Aesop fable "The Tortoise and the Hare". But even more directly, it is Avery's parody of the 1934 Disney Silly Symphony, The Tortoise and the Hare. Interestingly, Max Hare from the earlier Disney film is often cited as one of the inspirations behind Bugs Bunny.
Avery left Warner Bros. before he could produce any new cartoons featuring Cecil. However, he introduced a similar character in 1943, Droopy Dog. Droopy would even take some of his tricks from his slow-and-steady predecessor, such as using his relatives to help him outsmart a wolf.