Translation:Don't send me text messages again!
别 - don't do it
别再 - don't do it again
别...了- stop doing it (already happening) or a suggestion not to start
The pattern 别⋯⋯了 (bié... le) is all you need to tell someone to STOP DOING THAT (which they're already doing).
The "别 verb 了“ pattern can also be used to negate the other person's suggestion or try to change their idea. The difference between this usage and the previous example is that the action has not happened yet.