Are we talking about a common soldier during a battle or just an assassination-like attempt? I've seen the first answered a few times and can link to those if that's what you mean.

I'm not sure about saxon England, but if the notion of sovereignty was similar to France later on I'd say there's a strong possibility that they would be brutally tortured. Michel Foucault's Discipline and Punish opens with a very long and graphic description of the execution of a regicide named Damiens in France before the French Revolution, spanning several pages. It's fairly hair-raising stuff: Damiens was publicly tortured in multiple ways, including being covered in boiling pitch, torn apart with pincers, unsuccessfully quartered (the executioner resorted to just sawing off bits of flesh), and so on. Foucault points out that the theatrical aspect of the punishment exceeded even any rational concern with inflicting pain or feasibility of the methods used, and interprets the event as a kind of theatrical revenge played out on the body of the condemned.

I can't recall any assassination attempts in AS England of royals by commoners - the closest might be the death of Edward the martyr.

The first real explicit definition of high treason comes from Alfred's Dooms, which states the penalties:

If anyone plots against the king's life, of himself, or by harboring outlaws or faithless men in the king's service, let him be liable in his life and in all that he has. 1. If he wishes to prove himself true, let him do so according to the king's wergeld (i.e., by an oath equal to the kin'g's wergeld). 2. So, also, we ordain for all degrees, whether ceorl or eorl. He, who plots against his lord's life, shall be liable in his life to his lord, as well as in all that he has, or he shall prove himself true according to his lord's wer.

And that's pretty much how things were done - Anglo-Saxon kings preferred to fine or mutilate or exile rather than put to death. If death was the route, then it was either by hanging or by decapitation, both of which can be found in the archaeological record (Beowulf has two mentions of gallows).

Torture wasn't an Anglo-Saxon thing as far as I've read, and couldn't be used to determine truth. There are some later manuscripts which appear to show some sort of mutilation such as Harley's Psalter where you can see some of the men with their feet cut off, but this is also attested to in the archeaological record, and it's not always certain whether this is done pre-execution or post.