This is the first short featuring Sam Sheepdog and Ralph Wolf and is the prototype for the following 6 episodes. The title is a play on the expression "Don't Give Up the Ship".
Ralph's first plan is to trick Sam into going home early, by turning the time on the punch clock forward and setting the whistle off. Sam is initially tricked into thinking that the whistle indicated quitting time, punches out, and heads home. However, he quickly notices the clock on a church steeple with its bells chiming and hurries back to see Ralph carrying a comically large pile of sheep. Sam Sheepdog suddenly appears behind a tree and breaks a tree branch over Ralph's head, driving Ralph into the ground (although this all happens off-screen, and the viewer is left to figure out what happened after seeing the after effects).
Ralph's second attempt involves disguising himself as a bush. After stealing a sheep and starting to run away, he runs past Sam, who himself is disguised as a tree and starts to follow Ralph. Sam hits Ralph on the head with a branch, leaving Ralph very confused and with a large lump on his head. After attempting to run further, this occurs once more, and Ralph is left with two lumps on his head. Ralph then gives up and carries the sheep back to the field as Sam impatiently taps his foot (disguised as a tree root).
For Ralph's third attempt, he reads a book of Greek myths which explains that Pan would "lull shepherds to sleep with the music of his pipes and then steal the sheep." Disguising himself as Pan, Ralph attempts to lull Sam to sleep with a flute, but Sam merely punches Ralph in the face and Ralph stumbles away and continues to play his song, out of tune.
Ralph's fourth attempt involves tunnelling under the field and pulling each sheep down through very small holes. This is mostly successful, until Ralph unwittingly pulls Sam underground and gets punched in the face. Ralph politely returns all the sheep and refills his tunnel.
In Ralph's next attempt, he places an Acme product behind Sam, labelled "One Acme wild-cat - Handle with care". Ralph carefully opens the box with a rope from a distance behind another hill, but the wildcat simply runs toward Ralph and maims him.
Ralph's sixth attempt is to swing on a rope over the field and snatch a sheep. Unfortunately, he unwittingly snatches Sam out of the flock. After realizing this, he leaves Sam at the bottom of the rope and climbs to the branch that the rope is tied to and saws the end of the branch off. After seemingly sending Sam crashing to the ground, Sam appears on further down the branch and saws it off at that point, sending Ralph falling. After Ralph seemingly hits the ground, he appears at the start of the branch. This gag continues until Sam is on the end of a cliff and Ralph uses a pick axe to detach the edge of the cliff and send Sam falling. The cartoon then disobeys gravity and leaves Sam's piece of earth floating in the air, as the rest of the cliff which Ralph is standing on falls down.
Ralph's next and seemingly final attempt is to snatch a sheep which is drinking from edge of a lake. He uses a hollow rush to swim through the lake unnoticed. Sam notices the rush sticking out of the water and drops a stick of dynamite into it. Ralph surfaces and then sinks like a ship.
At the end of the short, Sam walks toward the punch clock as his replacement punches in and greets him. Sam hits him over the head with a plank, and the viewers see that the replacement turns out to be Ralph in a disguise. As Sam begins spanking Ralph with the club, Sam's real replacement shows up and takes over for him, continuing to spank Ralph.
On ABC the end of the short where Sam spanks Ralph as the real Fred Sheepdog punched in was removed.