I've never heard that. The closest thing I can recall is during WWI something about cutting a sawtooth pattern on the back of your bayonet. Probably not an official policy, but more like guys you just charged with that thing not taking prisoners because of the more terrible wound that bayonet would make. I don't know if that was a real thing or just made up later.
I think the story was garbled in translation. There was an extensive and vicious propaganda campaign against "German Kultur", creating a beastly image of Germany and Germans. If the Allies had thought of Baby Cannibalism I am sure that charge would have been laid against the Germans. I can recall claims that the Iraqi's turned off baby respirators in Kuwait, and that propaganda campaign lasted around 6 months, imagine what the propaganda was like in a four year long world war!
As it was, anything , true or not, anything that could make the Germans more beastly was put into the popular culture of the allies. The saw back bayonet was one of the things that was used to defame Germans. Sawback bayonets were issued to Engineer battallions as a dual use item: it had a saw which could cut wood. I have a Swiss sawback, the teeth are very sharp, still, I think it is too wide to be a useful saw. I don't remember if the British and French had sawbacks, it is probable they did, but that would have been forgotten, along with all the sawbacks in issue elsewhere, because it made for a good atrocity story against the Germans. It was said at the time that the sawback was proof of the nasty evil nature of Germans, it was claimed the saw teeth were there to make a bayonet wound worse.
I am certain the teeth would not have made any bayonet wound any better, but the teeth were there to cut wood.
Based on reading actual accounts of the times, diaries, recollections, etc, if a German was caught with a sawback, he was shot.
Lots of prisoners were shot by the British for lesser reasons, such as escorts deciding it was too much work to walk across muddy bogs on a cold day and deliver prisoners to the rear. Many such incidents were committed just at the point of surrender and after surrender in both world wars. I am have heard family stories of American's shooting Germans in WW2, and there is a reason why we took very few Japanese prisoners. A Uncle of mine was told to get rid of his Japanese prisoner or he would have to pull KP. He did not pull KP, so you can guess what happened.
Though, except for Fort Pillow, and the shooting of black Soldiers by Confederates, the Civil War has surprisingly few atrocity stories.
Anti German feelings were raised so high in WW1 that having a German name could get you beaten in the US!
As for swords, the Confederates were well known for keeping theirs sharp! Many Union swords are dull. Ninety nine percent of the sharp edges on period swords were done by enthusiasts after the sword was sold on the civilian market. Service swords were dulled after a conflict because of accidents. One story I read, of a new British Cavalry officer, he was in a warlike mood and sharpened his sword prior to mounted sword practice. He managed to cut his horse's ear off!