Historically, how effective were cutting attacks from swords? While I am sure being slashed with a sword is not good, it seems like thrusting attacks and blunt trauma would be more likely to be lethal or produce disabling wounds. It doesn't take too much armour to mitigate the impact of a slashing attack. I could see a sword still producing some blunt trauma upon hitting a piece of light armour (it is still a lot of force concentrated in a small area).
On unarmoured opponents something like a flanged mace would be devastating with even non-lethal hits producing broken bones and other disabling injuries. Blunt weapons are also pretty effective against armour. Thrusting weapons, while somewhat mitigated by armour, are easy to use and cheap to make. A solid poke pretty much anywhere in the chest or torso area carries a pretty good chance of dealing a lethal blow.
Cutting with a sword must have been somewhat effective (otherwise why would they have made swords with cutting edges for so long), but it seems less likely to kill or maim with same efficacy a thrust would or a just good smack from a blunt weapon of some sort.
I don't really have any experience with swords, but I have chopped things with a heavy machete and razor-sharp (or at least pretty close to) camping knife so I am at least dimly aware of the mechanics.
Wounds that penetrate the skull or body and enter the brain or the thoracic or abdominal cavity are often fatal. Wounds to the brain and heart are often promptly fatal. For other wounds to the thoracic and abdominal cavities (and non-immediately fatal wounds to the brain), the main causes of death are bleeding, collapsed lungs, and infection. Note that both cuts and thrusts can cause such wounds, and significant numbers of cutting wounds to the brain on the Medieval battlefield are evident from skeletons. Penetrating wounds to the body are more likely to be from thrusts and arrows.
However, note that:
The torso and head are often well-protected on the battlefield. These are the most commonly armoured portions of the body, and the best-armoured portions of the body (e.g., while plate armour over the arms might be under 1mm thick, a breastplate might be 2-3mm thick). Much body armour will stop arrows, spears, sword thrusts, sword cuts. The main vulnerability would be to deliberate stabbing in gaps in the armour with daggers while wrestling, and firearms. Heavy bows and crossbows might penetrate at short range (but might not), and couched lances might penetrate (or might not).
In hand-to-hand combat, the torso and head are further than the extremities, and are a more difficult target to reach with a sword. If the torso and head are well protected by armour, the main target for a sword would be the limbs.
Eventual death from infection and death from blood loss after many minutes are of less utility in hand-to-hand combat on the battlefield than immediate incapacitation.
So, given that for swords, arms and legs are often more likely targets, one needs to consider the effectiveness of cut vs thrust on arms and legs. While a thrust to an arm or leg can do significant damage, it can also fail to incapacitate. Cuts to the arms and legs can also fail to incapacitate, but they offer much more likelihood of immediate incapacitation of the limb through amputation. For example, Fig 9 in Mitchell (2004) shows a wound to the left arm which severed the arm at the elbow; this is one of the skeletons of the defenders of the castle at Jacob's Ford which fell to Saladin in 1179.
The common lack of short term incapacitation from thrusts, even thrusts to the torso and head, can be seen in various accounts of duels with rapiers and smallswords, where opponents run through continue to fight. One famous extreme example is the duel between Bazanez and Lagarde Valois (or de la Garde Valon, as given by Hutton (2012)), the latter a famous duellist. In their duel with rapier and dagger, Lagarde hit first with a thrust to the forehead, which failed to penetrate Bazanez's skull. Second and third blood also went to Lagarde, who hit Bazanez with thrusts that penetrated deep into his body. Upon which, Bazanez dropped his sword and closed with Lagarde in a rush, and stabbed him in the neck. They wrestle, and fall, and Bazanez being uppermost, continued to stab Lagarde, stabbing him at least 14 times in the body with his dagger. This killed Lagarde, but not before he bit off a substantial part of Bazanez's chin (and according to some versions, fractured Babanez's skull with the pommel of his sword). Hutton gives one version of this, and other similar versions can be found in other sources.
There are many other examples. To give just one more showing failure of thrusts to incapacitate, from the Victoria Cross citation for Naik Fazal Din, for an action in Burma in 1945:
Naik Fazal Din went to the Bren gunner's assistance immediately but, in doing so, was run through the chest by the officer, the sword point appearing through his back. On the Japanese officer withdrawing his sword, Naik Fazal Din, despite his terrible wound, tore the sword from the officer and killed him with it. He then attacked a Japanese other rank and also killed him. He then went to the assistance of a sepoy of his section who was struggling with another Japanese and killed the latter with the sword. Then, waving the sword, he continued to encourage his men. He staggered to Platoon Headquarters, about 25 yards away, to make a report and collapsed. He died soon after reaching the Regimental Aid Post.
While he did die from the wound, he was able to disarm the swordsman, and kill him and two other enemy soldiers with the sword which had run him through.
Of course, one can find many accounts of cuts failing to incapacitate as well. It can be noted that incapacitation of a limb does not necessarily stop a determined fighter. Also from a Burma VC citation, this time for George Albert Cairns, for an action in 1944:
During this action, in which Lieutenant CAIRNS took a foremost part, he was attacked by a Japanese officer, who, with his sword, hacked off Lieutenant CAIRNS left arm. Lieutenant CAIRNS killed this Officer; picked up the sword and continued to lead his men in the attack and slashing left and right with the captured sword killed and wounded several Japanese before he himself fell to the ground. Lieutenant CAIRNS subsequently died from his wounds.
An eyewitness account of this action, from a letter, notes that Cairns was not only wounded in the arm, the arm being almost severed, but had also been bayoneted twice in the torso:
George Cairns and a Jap were struggling and choking on the ground, and as I picked up a Jap rifle and climbed up towards them I saw George break free and, picking up a rifle bayonet, stab the Jap again and again like a madman. It was only when I got near that I saw he himself had already been bayoneted twice through the side and that his left arm was hanging on by a few strips of muscle. How he had found the strength to fight was a miracle, but the effort had been too much and he died the next morning.
In summary, it appears that thrusts may indeed be more lethal, considering infection risk, but cuts may well offer more chance of immediate incapacitation, especially with hits to the arms and legs. Neither thrusts nor cuts can be considered to have reliable stopping power.
References:
Hutton, A., The Sword Through the Centuries, Courier Corporation, 2012 (and various other reprints are available).
MacInnes, I., 2018. “One man slashes, one slays, one warns, one wounds”: Injury and Death in Anglo-Scottish Combat, c. 1296-c. 1403. Mainz Historical Cultural Sciences, Volume 38, p.61-77.
Mitchell, P. D., Medicine in the Crusades: Warfare, Wounds and the Medieval Surgeon, Cambridge University Press, 2004. https://books.google.com/books?id=1GwIDzFxmkEC