After six months of relief on the idyllic island of Tahiti, where most of the men marry Tahitian natives, they must reluctantly leave after securing their breadfruit trees. It doesn't take long for Bligh's viciousness to be displayed again. The incident that triggers the famous mutiny on board is Bligh's insistence that the sick, elderly ship's Dr. Bacchus (Dudley Digges) come topside to witness the flogging of five crew members caught attempting to desert the ship and return to Tahiti. When the deathly-ill, alcoholic doctor dies while struggling in his effort to get up to the deck, Fletcher's restraint breaks. When he sees his men being beaten, he raises his fist and cries:

Now you've given your last command on this ship. We'll be men again if we hang for it.

Fletcher calls for mutiny, and the mutineers tie the Captain to the mast and taunt him. Christian saves Bligh from certain death at the hands of the mutineers, but refuses to give up the mutiny, charging Bligh with murder:

I'll take my chance against the law. You'll take yours against the sea.

The captain cannot believe that he is being cast adrift in an open boat with eighteen other men - Byam and several others who are not part of the mutiny remain on board due to lack of room in the boat.

Bligh: But you're taking my ship. My ship.
Christian: Your ship? The King's ship, you mean. And you're not fit to command it. Into the boat!

Bligh threatens to avenge the mutineers:

Casting me adrift thirty five hundred miles from a port of call. You're sending me to my doom, eh? Well, you're wrong, Christian! I'll take this boat, as she floats, to England if I must. I'll live to see you - all of ya - hanging from the highest yardarm in the British fleet!

Amazingly, with only limited supplies and a few nautical instruments, Bligh is able to navigate the small boat on a 49 day, 3,618 mile voyage to Timor in the Dutch East Indies. The mutineers return on The Bounty to the island of Tahiti where they live happily for many months. Christian marries Maimiti and Byam marries Tehani.

On another British frigate - The Pandora, Bligh takes command and returns a year later, vengefully determined to seek out the mutineers and other crew members who remained behind. In a hasty departure from the island, Fletcher Christian tells Byam that he accepts his fate:

When you're back in England with the fleet again, you'll hear the hue and cry against me. From now on, they'll spell mutiny with my name. I regret that.

Byam and five others who did not participate in the mutiny, initially overjoyed that they are soon to return to England, are charged with mutiny and placed in irons. Their protestations of loyalty are ignored. When Bligh's search for The Bounty is unsuccessful following the wreck of The Pandora on a reef, the few remaining survivors are eventually, after another open boat trip, brought back to England to stand trial. Meanwhile, Christian journeys to uninhabited Pitcairn Island [between Chile and Australia] to build new lives with the others, crashing and burning The Bounty so they can never leave.

In a mutiny/court-martial trial in England five years after sailing from Portsmouth, Midshipman Byam is called to testify. In a closing statement after he has been sentenced to hang, Byam discloses all the cruelties and injustices imposed by Bligh. In a memorable speech, he suggests an alternative to flogging while denouncing Captain Bligh:

These men don't ask for comfort. They don't ask for safety...They ask only (for) the freedom that England expects for every man. If one man among you believed that - one man! - he could command the fleets of England. He could sweep the seas for England if he called his men to their duty, not by flaying their backs but by lifting their hearts - their..., that's all.

Before Byam's sentence is carried out, the King pardons him with a reprieve, and he is triumphantly returned to service in the British Navy.