The Saxon Tales (and the TV adaptation, The Last Kingdom) take place during the reign of Alfred the Great (r. 871-899), which gives us a time and place in the larger and much more expansive period of the Viking Age (ca. 750-1070).

There's not much historical literature that survives from this period. Alfred seems to have sponsored the Anglo-Saxon Chronicle, which was apparently first put together sometime before 893, when it was first sent out in several copies across southern England. Alfred's friend Asser wrote a biography of Alfred, also completed in 893. Asser used the Anglo-Saxon Chronicle as his main source of information for before 887, and then he took a more literary turn, using Alfred's actions in recent events to reflect upon ideals of good Christian kingship.

Neither of these texts deals much with persons captured on the battlefield. They use a lot of stock language, and although I haven't done sufficient study to really prove this claim, it's my impression that the most common phrases are ones like holding the field, putting the enemy to flight, or ravaging the land. This is an interesting set of word choices, and it suggests that Alfred and his court were much more concerned with staking land claims than inflicting casualties or capturing soldiers. Whether they killed their captives or cut off their hands, or whatever else they might have done, I can't recall ever reading a reference to it in contemporary sources.

If we expand our focus to think more broadly about northwest Europe across the Viking Age, we can say a bit more. A classic study of annals in Ireland revealed that taking captives was in fact an important aspect of war during this period. Another classic study of early medieval slavery saw slave raiding as a cornerstone for Charlemagne's early career and particularly his wars against the Saxons, although it seems that Charlemagne and his descendants later struggled to call the shots in the slave markets. As time went by, vikings seem to have cornered the European slave market, with Scandinavia as a major hub redirecting slaves to points east and south.

France and England seem to have suffered especially during this period. An important account of Bristol around 1070 suggests that Ireland was also importing captives taken from England during this period. And the German missionary Ansgar who visited Scandinavia several times between 830 and 850 recorded what viking raids might look like. He reported how a Christian friend had warned his pagan companions of an impending raid:

See, your enemies are coming to destroy all that you have. They will lead away your wives and sons as captives, they will burn our city and town [Birka] and will destroy you with the sword. Of what advantage are your idols to you?

I think that's one of the best indicators we have. Men who were captured on the battlefield or during a raid would generally have been killed, whereas women and children were liable to be taken and traded or sold as slaves. It's tempting to say that Christians wouldn't do such things, although John Gillingham has convincingly argued that this was a major shift in Christian attitudes and social mores that didn't occur until after the Viking Age. And archaeologists have recently turned up what looks like a viking crew who were captured and brutally beheaded. The most likely scenario is that these vikings were defeated by the leader of a local fyrd, who retained a few of the captives' heads to show off as trophies to his Wessex king.

TLDR We don't have sources that let us speak definitively about Alfred, but it seems like it was better to run away from a battle than to try surrendering. Men who were captured would likely be killed, wheres women and children captured in wars or on raids would likely be taken as slaves for the market.