It introduces the character of Screwy Squirrel, who appears in only five cartoons. It actually starts with a very cute Disney-style forest scene showing a happy, singing little squirrel named Sammy. He is soon pushed aside however by Screwy Squirrel, who, apparently with nothing better to do, taunts a slow-witted bird dog named Meathead Dog into chasing him. The rest of the cartoon is an utterly insane chase, even for Tex Avery, in which Screwy continually gets the best of the poor dog.
Despite being an iconic character, Screwy appeared in only five cartoons, possibly because he was just too mean.
- Alliterative Title: "Screwball Squirrel". The character is also sometimes called "Screwball Squirrel" instead of Screwy.
- Bait-and-Switch: Screwy is insulting Meatball over the phone and is about to curse him out when he apologizes to the audience and closes the phone booth door so they won't hear what he's about to say. Instead of seeing him hurl obscenities as was implied, we see Screwy blow a raspberry into the phone.
- Big Ball of Violence: At the end Screwy, Meathead, and their twins attack Sammy Squirrel for interrupting the cartoon.Sammy: My cartoon would have been cuter.
Screwy, Meathead and their twins: Oh, brother, NOT THAT! (cue Big Ball of Violence)
- Blowing a Raspberry: Screwy does this over the phone when trying to get Meathead angry enough to chase him. It works.
- Broken Record: At one point when Meathead is chasing Screwy the animation frames and music repeat over and over until Screwy moves the needle on the record.
- Disneyesque: The opening sequence isn't just cute and cuddly, it's Walt Disney's version of cute and cuddly, with a big-eyed happy squirrel named Sammy who's drawn to strongly resemble Thumper from Bambi.
- Dogs Hate Squirrels: Meathead Dog is initially an aversion, claiming he's a "bird dog" who never chases squirrels, but Screwy provokes him until he becomes a straight example.
- Efficient Displacement: One scene has Meathead Dog crashing into a tree and leaving a bend on the tree shaped just like his head.
- Fake-Out Opening: Starts out with a very cutely-drawn squirrel skipping through the forest and singing a song. Then, just when you think it's going to be a Disney-style cute and cuddly cartoon, Screwy jumps in and the whole thing goes sideways.
- Green Around the Gills: At one point Meathead chases Screwy to the beach and on to a wrecked ship. Screwy draws a picture of waves on a piece of paper, holds it outside a window, and moves it around. Sure enough Meathead gets sick and his whole body turns green. Right after this Screwy laughs at his cleverness as he bobs the picture around—until he makes himself turn green and rush off camera to vomit.
- Hammered into the Ground: Screwy takes his bat and hammers Meathead into the ground like a spike—and this after Meathead saved his life by catching him with the net!
- Iris Out: Played for a gag. Meathead begs for mercy, asking for the cartoon to be over. The Iris Out starts but Screwy grabs it, pulls it back open, and then tempts Meathead into one last challenge. Meathead is then run over by a train.
- Left the Background Music On: Along with the Broken Record gag above, Screwy is seen doing all the sound effects for Meatball rolling inside a barrel and crashing.
- Medium Awareness: Screwy first appears in the cartoon by greeting Sammy with an insolent question: "What kind of cartoon is this going to be anyway?" Later, he wonders what the next gag is supposed to be, so he lifts the corner of the cartoon to find himself under a tree. Screwy then takes his place under the tree and performs the next scene. At the end, Sammy returns and says "My cartoon would have been cuter."
- No Fourth Wall: Screwy addresses the audience repeatedly.
- The Not Catch: Played straight and then played with—the first time Screwy pretends to be catching Meathead Dog and pulls away the net at the last second. ("Too bad. Juuuust missed him! Hahahahahahaha!"). The second time, Screwy gets so caught up in pretending to catch the dog that he actually falls off a cliff himself, and Meathead (somehow) catches him. Screwy thanks him with a dozen blows to the head.
- Screwball Squirrel: This short is the Trope Namer. Screwy is an especially sociopathic example. Meathead Dog doesn't even want to chase Screwy—he's a bird dog! But Screwy taunts him into a chase, and then inflicts all sorts of punishment, from hammering Meathead into the ground to whacking him in the head with a bat to ripping his face off with flypaper, to eventually having Meathead run over by an oncoming train. This is Comedic Sociopathy that even Jerry wouldn't go for. Averted with Sammy, who's a nice, innocent squirrel (whom Screwy almost instantly beats up).
- Shout-Out: Among all the cute friends that Sammy says he's going to have fun times in the forest with is Barney Bear, star of his own series of MGM cartoons.
- Subverted Kids Show: We see a lovely forest scene and a cute squirrel picking up acorns. Then Screwy Squirrel appears and asks him what kind of picture this is going to be? The squirrel says it will be about him and his "cute, furry friends in the forest", whereupon Screwy groans "Oh, no, not that!" and takes him behind a tree where he beats him up.
- Twin Switch: At the end, Screwy reveals that he has a twin he used to fool Meatball. Then Meatball shows up with his twin to catch them both.