When you look at mass graves found at the site of battles there are three kinds of injuries.
1) The "crippling" injury. This is the one that robs your ability to get away and gets you killed. We have examples of swords going through leg bones, and in one case an axe blow that went straight through the thickest part of the foot, slicing it off.
2) Injuries to the arms and hands. Once people are down or cornered and they come in for the kill, people try to stop blows with their hands and arms, we have cases where there are dozens of injuries to the arms and hands, where people tried to defend themselves.
3) Head wounds and to a lesser degree chest wounds. Smashed skulls, massive lacerations to the face, puncture wounds, pieces of skill sliced off, blunt trauma and again this is rarely a clean kill and people will hit you a few times to make sure you are indeed dead. We also find wounds to the ribs often caused by spears or axe blows and cuts from swords though they are less common due to most soldiers wearing some kind of body armour whenever possible and the fact that a helmet is far more easy to remove than a breastplate or a coat of mail.
More importantly we find that a portion of those who died in battle have previous injuries that healed. Fused knee joint, severe injuries to the skull, broken bones that didn't reset and evidence of lacerations down to the bone that did eventually heal.
So it seems that people not only fought and got injured but lived to fight another day. And people rarely go down by simply dragging your sword edge across their body. They struggled, screamed, pleaded for their lives and struggled to the last moment before they had their heads smashed in.