Your question isn't very clear. From your own answer, I can tell better what you are trying to do:

public static String[] removeElements(String[] input, String deleteMe) {
    List result = new LinkedList();

    for(String item : input)
        if(!deleteMe.equals(item))
            result.add(item);

    return result.toArray(input);
}

NB: This is untested. Error checking is left as an exercise to the reader (I'd throw IllegalArgumentException if either input or deleteMe is null; an empty list on null list input doesn't make sense. Removing null Strings from the array might make sense, but I'll leave that as an exercise too; currently, it will throw an NPE when it tries to call equals on deleteMe if deleteMe is null.)

Choices I made here:

I used a LinkedList. Iteration should be just as fast, and you avoid any resizes, or allocating too big of a list if you end up deleting lots of elements. You could use an ArrayList, and set the initial size to the length of input. It likely wouldn't make much of a difference.