murder is a legal definition. ANd, in fact, you can kill someone illegally and not be guilty of murder, "Manslaughter" is another legal definition.
Anyway, killing someone just because they're "Bad" doesn't generally work for a heroic style character. There have to be reasons in text for doing it, and there has to be a lack of viable alternatives. Death and killing can show up in an uplifting book (apologies to the non-Mormons) but we see Teancum adn Gideon and Cap. Moroni, and the other Moroni, and Mormon, and Nephi and Benjamin and Mosiah all doing it, and they're all men of god, most of them prophets, and the Book of Mormon is still uplifting. the thing is they didn't take pleasure it in, they reveal they were even a little conflicted by it but didn't feel they had a choice, and they did it for very specific reasons. That's how it should work in any book if you want the reader to sympathize/empathize with the character.
of course, sometimes you can get away with ignoring the viable alternatives, if you've built up a LOT of sympathy and the reader wants revenge too. But I prefer not to do it that way, myself. That's not the sort of feeling I want to evoke.