The "spots" sound like necrosis. Typically when sponges get any kind of matter lodged in the tissues or air bubbles, it prevents that area from receiving much needed O2
. Most often this spells doom for the sponge unless the affected area can be safely cut away. The spots will continue to spread otherwise.
Before you start any major surgery, I would suggest posting a pic to be sure. If so, this must also be done under water as they can never be exposed to open air.
How are the tank specs and how was the sponge acclimated?