To reiterate, アカメが斬る (Akame ga Kiru) means "Akame cuts/slices/kills". Kiru also has another meaning: "to perform surgical incision", though the kanji is 切る in the case of this definition. This aligns well with the settings of the series: the goal of Akame and her group is to perform the necessary surgery on the corrupted empire by eliminating the tumors.
What is missing in the title are the objects, the targets that Akame kills. In episode 1, Tatsumi said 「俺が斬る」 (Ore ga Kiru), which means "let me kill (her)" or "I'll kill (her)". Even though there was no object specified, we could infer whom Tatsumi would kill. As for whom and what Akame kills, アカメが(Xを)斬る, the object X can be any of those in the chapter titles. Granted, it wasn't always Akame who did the killings, but she is actually a personification of Death (see explanation below) because her lethal and efficient one-cut-kill is befitting of Reaper's Scythe.
Does it mean that Akame is Death itself, or Akame is Dead (Not physically, but mentally - that she is dead inside).
Actually, that is my thought exactly. In episode 24,
Esdeath remarked that Akame is no longer human. It makes sense because Murasame's one-cut-kill doesn't work on non-human beings, or more precisely, beings without a beating heart, which is why Akame didn't die after cutting herself with it because she became Death. Also at the end, Akame said "I can only kill" because that is her newly acquired job as Death. Najenda and Akame, the only two survivors of Night Raid in the anime, actually symbolize Life and Death, as shown by them wearing capes of opposite colors and carrying out opposite roles of constructing and destroying for the new empire.
Akame was just an ordinary member of Night Raid, yet the show is named after her. She wasn't the main Protagonist, she wasn't even the main Waifu!
Princess Mononoke is also named after San who is not the main protagonist, even though Hayao Miyazaki had originally preferred the title The Legend of Ashitaka and even went as far as to create a new kanji for legend (sekki). Although Akame is not the main protagonist, like San, she is still indispensable to the plot, especially in a symbolic way.
Why not name the series Ore ga Kiru or Tatsumi ga Kiru? Well, because it wouldn't be as intriguing as Akame ga Kiru. The readers would get hooked on who is Akame and why does she have red eyes, the literal meaning of akame. (In Chinese, it so happens that there is a phrase 殺紅了眼 to describe a person who goes berserk from killing too many people that his eyes turn red.) It's red eyes and not black eyes because the story is full of the so-called "leftist" ideas, hence the oft regarded color of the left. Subjectivity aside, the ordering also matters: a is both the first letter in the English alphabet and the first character in Gojuuon, so Akame ga Kiru will pop up earlier in searches than the alternatives.