The death of Judas is a familiar crux. We have two accounts in Matthew and Acts. At least superficially, these seem to describes two different ways of dying.
How these are two be harmonized is anyone's guess. My own theory is that Judas hanged himself, then animal scavengers yanked his body down (e.g. dogs, jackals, a bear, a lion).
This is easy to visualize for anyone who's seen nature shows in which wildlife photographers string meat from a tree, then photograph predators attempting to pull it down. So I think that's an economical explanation.
However, an unbeliever will object that I'm guilty of special pleading. If it was anything other than the Bible, I'd just admit we have discrepant accounts.
So let's take a comparison. Mattathias Antigonus was the last Hasmonean king. He was predecessor to Herod the Great. Depending on how you count them, we have three or four different accounts of his demise:
These people Antony entrusted to a certain Herod to govern; but Antigonus he bound to a cross and flogged, — a punishment no other king had suffered at the hands of the Romans, — and afterwards slew him. Dio Cassius, Roman History, 22:6.
Now when Antony had received Antigonus as his captive, he determined to keep him against his triumph; but when he heard that the nation grew seditious, and that, out of their hatred to Herod, they continued to bear good-will to Antigonus, he resolved to behead him at Antioch, for otherwise the Jews could no way be brought to be quiet. And Strabo of Cappadocia attests to what I have said, when he thus speaks: "Antony ordered Antigonus the Jew to be brought to Antioch, and there to be beheaded. And this Antony seems to me to have been the very first man who beheaded a king... Josephus, Antiquities ,15.1.2 (8-9).
and he deprived many monarchs of their kingdoms, as, for instance, Antigonus the Jew, whom he brought forth and beheaded, though no other king before him had been so punished. Plutarch, Life of Antony, 36.11.
As you can see, Plutarch, Josephus, and Strabo (according to Josephus) all say that Marc Antony had Mattathias Antigonus beheaded. By contrast, Dio Cassius says Marc Antony had him crucified.
Now, these aren't strictly contradictory. Dio Cassius doesn't exactly say Mattathias Antigonus died by crucifixion. It indicates that he was slain after he was crucified–which is rather vague.
If, however, we approach these accounts with the same skepticism that unbelievers apply to Scripture, we wouldn't try to harmonize them. For one thing, isn't crucifixion and decapitation overkill? Moreover, why dispatch him before he dies from crucifixion? The whole point of scourging and crucifixion is to make your enemy die a slow, excruciating. To behead him before he succumbs would be counterproductive. Finally, his death by decapitation is multiply-attested, whereas Dio Cassius is the only source who says he was crucified. What are the odds that a man would both be crucified and beheaded?
Ah, but here's where the story gets even more interesting. We aren't confined to literary notices. There's archeological evidence that, as a matter of fact, Mattathias Antigonus did undergo both crucifixion and decapitation. In 1970, an ossuary was discovered in the Abba cave. The remains were identified as belonging to none other than Mattathias Antigonus.
On the one hand, the cut jaw and severed second vertebra indicate decapitation. On the other hand, the ossuary contains three hooked nails (used in crucifixion) with traces of human calcium.
Recently, that's has been confirmed by Yoel Elitzur and Israel Hershkovitz. As one scholar (Greg Doudna) summarizes the evidence:
There are the very clear and specific indications that this individual was both beheaded and nailed through the hands at the time of death. As I understand it, very few nails have been found inside any ossuaries (with the bones) in any case, and in no other case have nails been found attached to hand bones in an ossuary. And this particular individual was also fairly clearly beheaded (possibly with the executioner whacking twice to complete the job, per P. Smith’s analysis). The extremely unusual combination, with no other known parallel, of nails attached to hand bones and beheading corresponds specifically and exclusively to dual traditions of Antigonus Mattathias being hung up on a cross and flogged (Dio Cassius), and beheaded (Strabo). While that particular combination may have been done by Romans in cases not known to history, Antigonus Mattathias is the only case in which these dual traditions of these two particular kinds of death are recounted for the same person—the exact combination that turns up on a set of bones in an ossuary of a tomb with an Inscription referring to bones of one MTTY, of the approximate time as Antigonus Mattathias as independently established on dating grounds.
Now, the death of Antigonus Mattathias is at least as convoluted and antecedently unlikely as harmonizing the death of Judas in Matthew and Acts. Yet there's both documentary and paleoforensic evidence that that's what happened.
Incidentally, the reason Antigonus Mattathias might have been beheaded after he was crucified was to expedite his death. Unless a corpse was buried before sunset, it defiled the land (Deut 21:22-23). Marc Antony may have been forced to accede to Jewish sensibilities in that respect.