I took a Latin course a few years ago, and now I'm trying my hand for a friend's tattoo.
Is my translation of the title correct?
English: Out of my death, new life.
Latin attempt: Ex mei mortis novae vitae.
Your initial version is quite good! There are just a few case errors.
Ex (or ē if you prefer) takes the ablative case, which here would be morte meā. And the "new life" should be in the nominative case: vīta nova.
I'm not entirely sure whether the Romans would say "my death" (mors mea, ablative morte meā) or "the death of me" (mors meī, ablative morte meī). But the idiom morte suā morī "to die one's own death" (i.e, die of natural causes) makes me think mea. I asked a new question to be sure.
If you want a full sentence, you can also add the word venit "…comes" at the end, but this isn't necessary for a short saying or epigram.
All in all, my version would be:
Ex/ē morte meā, vīta nova [venit].
Unfortunately there aren't quite enough syllables to rearrange into a hexameter line, or even a pentameter.
The nouns and adjectives can be freely rearranged; I prefer to have each adjective following its respective noun, but especially in poetry you can mix up the words as much as you like (so long as ex/ē comes before morte) and it'll still be understood.
Similarly, the choice between ex and ē is purely stylistic, as is the decision to include or leave off the macrons (marks over long vowels). I prefer ex and including macrons, but that's nothing more than a personal preference.