Jerrilyn has given u an excellent answer. On organza or tulle I use tear away on bottom & Wss on top(2 layers of WSS. *
I always use WSS (the vilene type)when I embroider on organze, After finshed you have to rins it out. Good Luck
Is your needle a ball point or a sharp? A sharp may be cutting the cotton. You can also use a tear away and just be certain to remove everything left after stitching. The other option is to use the "fabric type" wash away and run one piece in one direction adn the other piece in the other direction as in North/south and east/west. :)