Easiest way I am aware of is to use XFer mode processing from the Graphics package. Function below cuts region starting from (30,30) till (100,100) to the 320x480 image loaded from resources. Adapt coordinates to change dynamically:
private Bitmap cropBitmap1() {
Bitmap bmp2 = BitmapFactory.decodeResource(this.getResources(), R.drawable.image1);
Bitmap bmOverlay = Bitmap.createBitmap(320, 480, Bitmap.Config.ARGB_8888);
Paint paint = new Paint();
paint.setXfermode(new PorterDuffXfermode(Mode.CLEAR));
Canvas canvas = new Canvas(bmOverlay);
canvas.drawBitmap(bmp2, 0, 0, null);
canvas.drawRect(30, 30, 100, 100, paint);
return bmOverlay;
}