Ok, don't panic first of all!
Most likely this will pass through his system either by vomiting it back up or pooping it out. It may take a while, but he should be fine.
Was there any kind of chemical on the sponge? Like soap, pinesole, bleach, ect. I'm talking as if the sponge was just soaked in it and then he ate it. If the sponge was rinsed well before ingesting, you should be ok. If he ate it including chemicals, you need to contact your vet about the chemical type and how much he ingested. You will most likely have to take him in as most household chemicals are very dangerous especially in pups.
If there was no chemicals on sponge:
If he vomits the pieces back up, as gross as this will sound, try to make a whole sponge again. If you have all or most of the pieces, you should be out of the woods.
With sponges and other "non-food" objects, they can have a tendency to cause a blockage in the intestinal track. So you do need to keep a close eye on him. If his abdomen becomes tender, if he is trying to poop, but can't, if there is blood in vomit or stool, if anytime he eats or drinks, but throws it right back up, he could have a blockage and should be seen as soon as possible.
Like I said, you should be okay, and everything should be fine, you just need to keep a close eye on him for a few days. If he is throwing up for more than a day, he needs to get checked out.
If there is anything else I can help you with, please let me know. If you feel I've answered your question, please, don't forget to click "Accept". Bonuses are always welcomed!