An allegorical reason as to why the Shredder is named "the Shredder".

In the references to artists within the series' eponymous characters, the Shredder represents the destruction of artistic work, this "shredding", manifested in the series through the conflicts he finds himself with the Turtles.

As to how he can shred marble statues, I am not particularly certain of. He must be a stack of dynamite wearing his sleeping clothes or whatnot.

 

Eastman and Laird got the idea for The Shredder's armor late one evening after the two creators had been drinking. Kevin was drying dishes and came across a triangular cheese grater, he put the cheese-grater on his arm and said, "Could you imagine a character with weapons on his arms like this?". He said how it would be awesome to have a villain called, "The Grater" and Peter responded with, "How about the Shredder?". The next morning the two of them put their pens to paper and actually created the infamous character we know today.

 

The cheese grater in question would be considered a sort of Deus Ex Machina. In the wake of their descent into drinking themselves to sleep all night, the wonderful cheese grater appeared to patch up the story. The cheese grater, and the factor of Kevin placing the cheese grater on his arm, was a representation of the advent of Modernism in the art world of today.

Through subconscious psychological tying, they used the Shredder as a character to allegorically represent Modernism in the face of classical Renaissance art, essentially old and more contemporary art, portrayed through the Turtles and their respective nomenclature.

 

I thought I got the name because I was a wicked guitar player...