Yes cruise ships do dump poop out into the ocean when they are at least 12 miles away from land.
Cruise ships are allowed to dump poop and other human waste as well as gray water out into the ocean once they are 12 miles away from land.
If they are at port the sewage can be dumped into the ocean but it must be treated first.
But out in the ocean far away from land the sewage can be dumped as well as the grey water can be dumped untreated.
When you flush the toilet on a cruise ship or use the sinks, showers etc the water goes into a sewage tank underneath the rooms in the ship.
The cruise ships sewage tanks are in the bowels of the cruise ship and they have ways of treating the sewage before it's released.
The cruise ship can release the sewage though untreated if they are 12 miles away from land so they can dump the untreated sewage into the ocean as they are traveling down the ocean.
That seems gross but it's not really a bad thing as the sewage will be naturally treated in the ocean just like when sewage is on the ground the earth naturally treats the urine and poop.
So cruise ships do dump human waste into the ocean as well as foods scraps and sometimes other trash.