生 generally means “life”; “birth” is incidental to that. 命 also means “life” (primarily; in Japanese at least, it also means “[an] order” or “destiny”)
That is with individual meanings. If you should attempt to put them together, it will not make a hell of a lot of sense. 生命 is another word for “life”, for one thing. Kanji themes do not often come in threes. Always nice even twos or fours.
Also, just doing my duty as an azn on teh interbutt, 〜♪
I may just be an old-fashioned fuddy-duddy, but I strongly discourage people from getting this kind of ink, as in many parts of Asia (Japan in particular), tattoos still have a strong association with organized crime. 死 in particular is pretty taboo.