The Vorpal swords originate from "Jabberwocky"
Lewis Carrol's children's book "Through the Looking Glass", contains a nonsense poem called "Jabberwocky", which is full of arcane and unusual words. Alice finds it in a book written in a seemingly unintelligible language. Realizing that she is traveling through an inverted world, she recognizes that the verses on the pages are written in mirror-writing. She holds a mirror to one of the poems and reads the reflected verse of "Jabberwocky".
In the poem, a boy takes a vorpal sword and slays the Jabberwock, a horrible monster:
He took his vorpal sword in hand:
Long time the manxome foe he sought—
So rested he by the Tumtum tree,
And stood awhile in thought.
And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
One, two! One, two! And through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.
The poem depicts the vorpal sword as a weapon that can slice "through and through" and apparently decapitate the monster. It actually does not say it does that. The boy could cut off the head of the dead monster after he killed it, to bring back as a trophy.
Although it is not explicitly said that the sword chopped off the head, the line about the boy returning with the dead monsters head follows right after slicing through, so it is easy to make that connection, and apparently Gary Gygax did.
There is no other historic usage of the word vorpal that could further explain what it means. It looks like Carroll just invented the word. Martin Gardner, in "The Annotated Alice" reports that Carroll said he could not explain this word (while he explained various other words in the poem). Interestingly, the Collin's Dictionary, defines vorpal to just mean "fatal", and cites its first measurable appearance in literature as 1872, the year after "Through the Looking Glass" was published.
The first Vorpal Sword in Gaming starred in Greyhawk
Gygax turned Lewis Carroll's books into two special levels1 of his original Castle Greyhawk home game that was the testing ground for the D&D rules he published. He included the Vorpal Blade in random loot tables as the result if you rolled a 00 on a d100, and published it in Supplement 1: Greyhawk (1975), where he defined it like this:
Sword of Sharpness: This is another Holy Sword, and although it has only a +1 bonus hit probability, any attack employing it which scores 20% (4 or better), over the required number, or a 19 or 20 in any event, indicates it has severed a limb or a neck — in cases of multiple possibilities assign
probabilities and dice to see what the result is. (...)
Vorpal Blade: The Vorpal Blade differs from a Sword of Sharpness in several
- its bonus hit probability is +2;
- it needs only 10% over the required score to hit, or an 18 through 20 in any event to sever, and it will always sever the neck; and
- it will perform in the hands of any Lawful fighter, although it requires a Paladin in order to act in its anti-magic capacity.
Clearly, he read the poem as the sword having a penchant for chopping off heads.
1 Coincidentally these are the only levels of that famous dungeon that were ever published by TSR, EX1 Dungeonland, and EX2 The Land Behind the Magic Mirror -- the latter one contains a vorpal blade (p. 19).