We think that Mumming happened in other parts of early Germanic or Celtic Europe too, but it really hung on in England, so that’s where we go to study it. We only have written descriptions of Mumming scripts since the 18th century.
To study the story, we fall back on principles similar to principles of New Testament scholarship, because the problem is similar. In both cases, there are many copies of something, but the original is lost. You have to look at the many versions to work out what the original had looked like. You look for things that the versions have in common, things that make no sense (and therefore might be “corrected” in some versions, which would lose the original).
The versions all have in common a death, and a cure that brings the dead person back to life. They all have some kind of dance, most often including the sword used for the execution. The man who carries out the execution is virile, a champion. The victim is weak or a hated enemy. The script is a rhymed verse, and the players stop and collect money from the audience. Additionally, what all versions have in common is that they seem to incorporate change as a function of the story itself.
What did it originally look like? Perhaps at first it had a real victim, a captured enemy, and the warlord killed him with a sword to bless the spring. It might not have been so literal. Perhaps a man dressed as Tyr the Great Boar, lord of swords and fertility, mock-executed another man who represented farming (or something). But that victim was someone we needed! So perhaps a real shaman or someone dressed as one came in to raise the victim from the dead. And everyone rejoiced, giving gifts to the players (or perhaps just the shaman?). It was probably an early spring ritual, but it gradually became just the “folk drama” that could be done other times too.
In modern versions, the Narrator, who speaks in verse, is often Father Christmas. He calls out for a champion, and it’s usually St. George the Dragonslayer. The enemy became a Muslim during the Crusades, and by the 18th century, he was often “The Turk” with a turban. St. George and the Turk fight with swords, hopping and dancing. The Turk always falls, and he dies. The Narrator calls out for a Doctor! and a Doctor appears! he gives a cure to the Turk, who is restored to life. It’s likely that this has been the essential story for over 1000 years. the Turk’s being raised back to life makes no sense, so it’s probably original.
If someone wants to do a version with the basic roles relabeled to form some sort of satire, they can. Local groups go from pub to pub, putting on their little show while collecting cash in a can. Seen one Mummer story, seen them all? That’s the problem, how to freshen it up while keeping it the same.