Death's scythe is one of the two sharpest objects in existence. It is capable of slicing air, shadows and even time. Most importantly, it is designed to sever souls from their mortal shells. The blade is almost transparent, but glows blue thanks to the energy released by atoms splitting on its edge (thanks to the idiosyncrasies of Discworld physics, this does not cause the nuclear obliteration of a vast area).
Like most aspects of Death's existence, it is a metaphor. The concept of Death originated in rural communities, who saw the idea of a reaper as an appropriate way of looking at the process. In Reaper Man, this came in very handy, as it meant that Death was a dab hand at collecting the harvest on Miss Renata Flitworth's farm.
The scythe is Death's preferred tool, but for kings he has a similarly bladed sword. The sword has had a part to play in a few scenes across the canon, most notably in Hogfather when Mr Teatime tries to use it on Death's granddaughter. On occasions where he is called upon to perform what might be "quality control checks" on how the otherwise impersonal process of death is working itself out in other lifeforms (where in routine circumstances Death is not usually called upon to attend in person), he uses tools appropriate to the task at hand. He has been known to carry what looks like a jeweller's tool-roll, containing microscythes and very small blades appropriate to the species in question. We see this in Hogfather, where the process of life and death is happening among very simple plants and animals living around a volcanic vent on the abyssal sea floor. (We also note that Death takes a very direct, possibly hyperspatial, route home to his domain, after performing this particular check.)
For larger animals, such as the dying swan encountered in Maskerade, Death employs the usual scythe.
We know there is one enormous lifetimer with a turtle delicately engraved on it, (possibly flanked by four slightly smaller ones bearing a pachyderm device). What sort of professional tool will Death bring to bear here, when the time comes? The conventional scythe-or-sword somehow doesn't feel adequate.
In Reaper Man, thinking he might fight back against the New Death, Death (Bill Door) sharpens a scythe blade. First on a grindstone, then on an oilstone, then on a steel. It was too blunt. Miss Flitworth supplied, from her rag bag, satin, then silk, finest white silk, never worn (from her wedding dress). It was still blunt. Then it was sharpened on cobweb. Then on the breeze at dawn. Finally, on the light of the new day (Corgi PB p. 149). Bill Door made a new handle for the blade – not a straight one, such as they use in the plains, but the heavy, double-curved handle of the mountains. Later he took the whole scythe to the village forge, and paid Ned Simnel a farthing to destroy it for him in the forge furnace. “I want it killed ”, he said, so that it could be available to him in the realm between life and afterlife, where he would meet the New Death (p. 172).
Simnel, who was constructing the Combination Harvester, could not bring himself to destroy the extraordinary blade, so when Bill Door's time had run out and the New Death appeared, he had to take whatever came to hand. He found the scythe he had carried out Miss Flitworth’s harvest with. The ghostly form of Bill Door could not lift that weapon, but when Miss Flitworth gave him some of her own time, he was able to wield it, and the worn blade “snarled through the air, rage and vengeance giving it an edge beyond any definition of sharpness” (p. 231).
The haughty and arrogant New Death is described as having an implement to hand which which may, at some point in its evolution, have incorporated aspects of a scythe. The inference here is that the tool used by the New Death is as sterile, clean, and clinical as a scalpel used for a minor surgical operation, or perhaps as clinically functional as a vampire's fang, and which has as much of a "human touch" for the luckless recipient. The clear implication is there that the New Death is to the Old Death exactly what the "Combination Harvester" is to the old-fashioned manual scythe for reaping corn: in fact, the New Death gives all the appearance of one who would quite happily use the metaphysical equivalent of a combined harvester for reaping souls. But in extremis, in the ensuing clash of working philosophies, the New Death is vanquished by the old-fashioned scythe...