Yes, shred is in the scrabble dictionary

...and is worth 8 points by itself if you played it.

Shred Definition

noun

A long irregular strip that is cut or torn off.
A small amount; a particle: not a shred of evidence.
A long narrow strip cut or torn off.
A , damaged, or ruined condition .

verb-transitive

To cut or tear into shreds.

verb

To cut off.
To cut or tear into .
To come apart in or break up into shreds.