General tearing:
* Rip
* Tear
* Cut
* Mangle
* Disintegrate
* Fragment
* Splinter
Shredding to small pieces:
* Pulverize
* Mince
* Chop
* Dice
Shredding documents:
* Destroy
* Dispose of
* Decimate
* Annihilate
Shredding meat or vegetables:
* Grate
* Slice
* Julienne
The best synonym will depend on the specific situation. For example, if you're talking about tearing a piece of paper, "rip" or "tear" would be appropriate. But if you're talking about destroying documents, "destroy" or "annihilate" might be a better choice.