Do you think it will be compartmentalized? It would take a couple of harpoons to sink our big boys because of watertight integrity. If this think is a great big banana boat it ought to go really easy. A MK48, there is a cool idea.
Let's take it for granted that this baby has at least a double hull, and watertight integrity is minimum of western standards and reserve buoyancy equals at least 1/4 of the ship's displacement. Of course, this also assumes decent damage control training and equipment. It's oiriginally Russian, which means it's probably overengineered to the nth degree.
A Harpoon, being a surface attack weapon, would leave massive holes and start some nasty fires, but the blast from a single one or even a pair might not be enough to cause severe damage to cause sinking. A Tomahawk, with a minimum 1,000 lb warhead would cause much more devestating damage. Still, it's not likely, given all the above factors, that the ship is automatically doomed.
A Mk. 48, however, exploded under the hull, is a different story. A pair would be better. The expectation of critical damage which cannot easily be repaired or countered is much greater in this scenario. Do not forget that a ship is most vulnerable below the waterline, not above. Break a keel or destroy steering or propulsion gear, and it's merely a floating target.
It does not automatically follow that a missile hit, above the waterline, would cause much critical damage to a ship that large.