Based on Jewish law, a person's Jewish status (for a non-convert) is determined through matrilineal descent. This means that one is only Jewish from birth if their mother was Jewish. And their mother was only Jewish if their mother was Jewish.
Based on this, a person can have seven out of eight great-grandparents who are Jewish, and still not be Jewish from birth (in the case where the mother's mother's mother was non-Jewish).
So even assuming that the DNA test was 100% conclusive as to your DNA being descended from Sephardic Jews (a separate discussion), having DNA that is related to a Jewish group says nothing about one's Jewish status (though it can tell you a lot about your ancestry).
For further information on matrilineal descent, take a look at the answers to this questionanswers to this question or this questionthis question or at one of these pages: 1, 2, 3