It's possible to leave the ship owing nothing but the tips. I doubt that very many people actually do it, and I'm not actually recommending that you do ALL these things, but it's possible.
Instead of using Disney's shore excursions, use the internet to search for your own fun. Take a watch and a cell phone in case you have any problem getting back to the ship on time; being left behind would be very expensive. You can book excursions with local agencies, seek out free beaches within walking distance of the pier, or you can stay onboard and enjoy the empty pool.
Drink free lemonaide and fruit punch instead of sodas (outside the dining room). Or book with
AAA and get a free soda mug.
Skip Palo, milkshakes, special coffees, and alcoholic drinks (or bring your own).
Bring your own camera so you can skip the professional pictures.
Bring plenty of film, batteries, suntan lotion, medicines, etc. These will cost you a fortune.
Skip the souvenier shops. They really didn't have much anyway. Ditto when you get off the ship. The kids can get a free tee shirt for participating in the show at the end.
Bring along a small cooler (and ziplocks) so you can take free room service sandwiches with you off the ship. Bring an empty water bottle to be refilled on Deck 9.
Bring a lanyard and an ID holder from home.
I'm sure there are many other ideas about saving money, but that's what I can think of right now.