On the question of murder. I would argue that Janeway did murder Tuvix.
1. She intended to do him injury (kill him) so there is malice aforethought.
2. There was no legal justification for his death.
Some other moral issues:
There is a moral difference between killing and letting die however in this case Janeway killed Tuvix rather than allowed him to die. His death was necessary not a side-effect of getting Neelix and Tuvok back.
Since Tuvok was a close personal friend of Janeway it seems very unethical of her not to excuse herself from making the decision on the grounds that her decision may (and almost certainly was) influenced by her desire to see Tuvok return.
The manner in which she informed Tuvix of her decision and how she carried out the lethal procedure almost seemed to be unethical. Watching the episode I got a strong sense of disapprobation coming from her, as if Tuvix was guilty (of not relinquishing his life to restore her friends, of cowardice or selfishness, or even as if he were to blame for the death of Neelix and Tuvok).
Concerning the doctor, he has the power to overrule a ship's captain on matters medical. A medic aboard a submarine (often a non-commissioned officer) can order a captain to surface the vessel. Since the procedure was medical and the procedure would put in the danger the life of a passenger aboard the ship, he could have ordered Janeway to desist. The doctor actually refused to the carry out the procedure but didn't exercise his power to prevent the captain.
The 2 lives are greater than 1 argument
Suppose a valuable member of the crew, say Tuvok, accidently steps into an alien machine. The crew discover that his strange machine traps whoever enters for two weeks and then terminates them. The only way to free the trapped individual is for two living beings to enter the machine. When they enter, the trapped individual (in this case Tuvok) is spat out, alive and well but the two are now trapped and die instantly.
This is a case of killing 2 to save 1. However, for those who beleive that Janeway should base her decision on what is best in terms for the most effective crew complement then sacrificing 2 less important crew members in exchange for 1 much more important crew member seems to be the solution. The best candidates on Voyager would be Ensign Samantha Wildman and her baby Naomi. Would Janeway be prepared to do this? If the moral dilemma is decided on seeking the most effective crew complement then she has to be.
A similar dilemma...
Suppose two crew members, a husband and wife, go on an away mission to a planet and accidently wander into an alien machine. This machine, unlike the one Tuvok stepped into in the above example, will only release the trapped individuals if 1 person biologically related to both people is thrown into the machine. The 2 year old son of these two crew members is aboard the Voyager. Is Janeway prepared to throw him into the machine to save his parents?
A final quandry...
The doctor and Kim discover a way to get Tuvok or
Neelix back. That is, the procedure will kill Tuvix and the molecules of either Tuvok or Neelix will be restored. Janeway can choose one of three options:
1. Do nothing and allow Tuvix to live.
2. Choose Tuvok to be restored (killing Tuvix and allowing Neelix to be lost forever)
3. Choose Neelix to be restored (killing Tuvix and allowing Tuvok to be lost forever)