As far as excursions go, yes you can save money by booking your excursions on your own. 70%? Doubtful, maybe 50% for some of the beach breaks or snorkel tours. But there are SOME tours that you can only get through the cruise lines, but most of them can be booked on your own on-line.
You give up the convenience of having the whole package (transportation, activity, and food costs) all done with a single purchase as you will have to arrange all of that yourself unless you book with a tour company that meets you at the ship (most do). You also give up the "insurance" of the ship waiting for you if your tour is late, (say the bus breaks down) but if you plan for leaving an extra hour or 2 of margin in your return time you can always grab alternate transport back to the ship.
If you are an experienced cruiser and/or you are used to traveling and booking things yourself you can save a good amount on excursions.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013