Is Throwing Joseph into the Pit Considered an Act of Murder

The Ramban writes that they threw Joseph into the pit so that there would be no bloodshed, and he would die on his own. It is difficult for me to understand, as they are essentially killing him by starvation.

See Sema (Siman 388, Subparagraph 35) that lowering into a pit where he would die of starvation is considered indirect causation and not considered murder by one's own hands. In the case of a person who is permitted to be caused death through advice and trickery but is forbidden to be killed by one's own hands, this is how it is done. However, the Ramban does not state that he would die of starvation, and it is possible that they gave him water and bread in very limited amounts, as explained in the Mishnah (Sanhedrin 81) regarding one who was punished and sinned again and killed without witnesses. He is placed in a confined space and given water and bread under pressure, and then barley bread until his stomach bursts on its own, because it is not permitted to kill him by one's own hands, but the court is permitted to cause him death.

Sema (Siman 388, Subparagraph 35).