You are thinking in terms of cutting but the answer has more to do with crushing (think hammer, not knife).
The size and mass of the iceberg that hit the Titanic can only be estimated, but the survivors’ accounts describe it looming over the foredeck of the ship — so 50 to 100 feet high, several times that long, and an unknown amount under the water. Because it was solid ice rather than mostly empty space like the Titanic, the iceberg could easily have massed far more than the ship.
On top of that, unlike a battleship of the period, Titanic’s hull was not actually designed to fend off impacts. It was designed to hold the ship together as economically as possible. In a collision between a very large iceberg and a large ship, the physics are not like a knife cutting through an object. The physics are more like a car driving into a wall at high speed. Whether it’s made of steel or plastic, the car’s structure will suffer from that impact.
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