Apart from the steel in the hull, which is probably of a pretty high quality, you will have non-ferrous materials such as aluminium, brass an copper throughout the ship, and they will most likely be worth more than the steel, weight-for-weight. I would imagine plastics etc will also be reclaimable and sell at a reasonable price. This is why navies have sold ships for scrap ever since they started building ironclads.
Prior to this, wooden ships were often broken down in such a fashion as to be rebuilt in a new shape. The Royal Navy was very fond of this methods to build 'new' ships when times were hard (most of the time in the 17th and 18th centuries). Old ships would go into dockyards to be broken up, but the keel and some basic structure would reappear with a new vessel built around them, carrying a new name. Both the RN and the French also constructed razees, which were obsolete two-decker ships-of-the-line with their upper gundecks cut off ('razed') to create very large and fast frigates.
Of course, an iron or dteel ship is much harder to modify in this way (unless converting a BC or cruiser hull to an aircraft carrier, for example), so navies tend to simply sell the ships to scrappers, who pay a price based upon the materials used in the ships construction. It's much easier and cheaper than a navy having all the kit to turn an old ship into a new one.