A method that returns an array with no duplicates
Wouldn't it be easier to just use:
public static class IntArrayProcessor {

    private Integer[] arr;

    public IntArrayProcessor(Integer[] arr) {
        this.arr = arr;
    }

    public Integer[] unique() {
        final Set&lt;Integer&gt; uniqueSet = new HashSet&lt;Integer&gt;(Arrays.asList(this.arr));
        return uniqueSet.toArray(new Integer[uniqueSet.size()]);
    }
}

I changed the method name from getSet() to the more descriptive unique().
This simply generates a hash set, which contains only the unique values of the array. The hash set (uniqueSet) is then converted from Set to Integer[], and returned.
Given that this is using built-in methods and objects, it would likely be faster than most custom implementations.
Notice that HashSet:

makes no guarantees as to the insertion order of the set; in particular it does not guarantee that the order will remain constant over time.
— HashSet documentation

If you need to keep insertion order, use LinkedHashSet as suggested in @mrblewog's comment. If you want to have the internal Set sorted, use SortedSet or TreeSet.
I also changed int[] to Integer[] so that it can be used with generics (generics do not support primitive types).