What was the general breakdown of casualties per their cause during American Civil War?
E.g. bullets vs. artillery vs. edged weapons vs. disease vs. natural death.
Did that breakdown change in meaningful way between the beginning and the end of the war?
You can get a breakdown of the major causes of death here.
Prior to the 20th century (possibly late 19th), the dominant cause of death in war was disease: the troops were in close quarters with unsanitary conditions and inadequate means of handling these. This number was followed by complications related to injuries actually suffered in battle — frequently one would get a small injury and it would get infected and kill the individual even though it would be trivial to heal the wound in better conditions.
Unfortunately, I cannot give you a specific breakdown of blade vs. bullet (and I suspect that it would be impossible to do so), but I will say that, based on the artillery technology of the time, it is fairly safe to say that discerning the difference between bullet and canon shot would be quite impossible. Even if you assume that there was a substantial interest in maintaining those records, there would not have been effort made to determine which injuries are post-mortem.
Bruce Catton's history and Shelby Foote's history should have the details. I cannot check as my copies are at home. From what I remember, it was pre-battle medical care and unsanitary conditions that killed the most soldiers. The first use of modern rifles with Napoleon tactics contributed to the hight number of dead on the battle field.
According to John Keegan "The Civil War", there was multiple factors for wounds and deaths, and there was no clear account of which weapon was the cause of casualties. However, there are some elements to answer this question.
First, yes, disease were the first cause of death. But one can consider them to be out of the count of combat casualties.
- Infantry shooting is supposed to be the main cause of casualties, since the record of the battles show most of the time that only shooters could stop an attack.
- Artillery was very useful and dangerous at the time. But it was mostly a threat on a tactical level: thus, when artillery started to fire at a unit, the unit quickly fell back or tried to take cover: artillery hampered its move, disorganized but did not create numerous casualties. Even more, artillery often fired on units on a friendly zone, which means that wounded soldiers could be rescued by nurses. It did not mean however, considering medical capacities of the time, that all wounded soldiers were saved
- Bayonnet and edge weapon: There were not that much edge-weapon engagements, even for cavalry units which mostly fought dismounted. However, some close quarter fights occured sometimes, and they often led to numerous casualties*
Infantry fire: Most of casualties, high proportion of dead
Artillery: Numerous casualties, not that much of them dead
Edge weapons: No numerous casualties overall, but an infantry unit in close quarter fight was promised to heavy losses
*However, such losses were caused by edge weapons in the close quarter fight as well as by other soldiers shooting in the mass