Here is a version as sung by the Deseret String Band (AKA the Bunkhouse Orchestra), a local old-time/cowboy group here in Utah. They credit it to the Cartwright Brothers, and the tune and at least the first verse is identical to the sound clip by them, the link posted by Guest Dale above.
In a far-off western country, where friends are few and dear,
And the cattle roam in thousands, and the skies are always clear,
We were rounding up one morning, and the work was almost done,
And the cattle all stampeded, 'twas a wild and maddened run.
The boss's little daughter was holding on one side,
She tried to check the cattle, 'twas a wild and dangerous ride.
Beneath the lass's saddle, early on that fatal morn,
I'd placed a scarlet blanket, a mistake I'll always mourn.
When the cattle saw that blanket, it piqued their maddened brain,
They bore down on the lassie, and death rode wild again.
The boss's little daughter rode the best horse all around,
But he stumbled in a dog hole, and threw her to the ground.
The cattle thundered toward her, and she surely would have died,
But someone spurred his cow horse like lightning to her side.
He leaned down from his pony, and caught her from the ground,
But the cinches broke beneath them and once more hurled them down.
From the dust sprang Utah Carroll, the blanket waving gay,
He led off at an angle, and the cattle came his way.
His task was then accomplished, and the child safe on the side,
He turned to face the cattle, now a wild and maddened tide.
His pistol flashed like lightning, and it sounded loud and clear,
He failed to stop the cattle, but he dropped the leading steer.
A thousand hooves a-pounding, and a thousand slashing horns,
Snuffed out the life of Utah, the bravest hero born.
In a far-off western country, where friends are few and near,
Stands a humble little headstone 'neath a sky that's always clear,
And the rancher's little daughter now often goes to pray,
For the man who died so freely to save her life that day.