One US government web site gives these instructions:
Every year the U.S. Treasury redeems over $30 million worth of mutilated currency. Do you know how to get damaged US money replaced?
The correct procedure for replacing US currency depends on how and how badly the money has been damaged.
According to the Bureau of Engraving and Printing, currency that has not been mutilated can be redeemed at a bank, while truly mutilated bills require special handling.
Not Mutilated Currency includes any bill that is CLEARLY more than one-half of the original bill, and does not require any special examination or investigation to determine its value. Examples of non-mutilated bills include those that are badly soiled, dirty, defaced, disintegrated, limp, torn or otherwise "worn out."
These bills should be exchanged through your local bank and processed by the Federal Reserve Bank.
Mutilated Currency is considered to be any bill NOT CLEARLY more than one-half of the original bill and/or requires special examination to determine its value. Most mutilated currency has been damaged by fire, flooding, chemicals, explosions, animals or insects. Another very common source of damage to currency is petrification or deterioration by burying.
Here's another similar set of instructions:
The U.S. Department of Treasury's Bureau of Engraving and Printing in Washington, D.C. redeems badly damaged currency as a public service. Around 30,000 customers submit an average of $30 million every year for replacement with fresh, new money. We're not only talking about bills that have been torn in half or defaced with mustaches added to the presidents' faces. We're talking serious damage! Find out what the U.S. Mint considers mutilated in this sidebar.
A stack of one year's worth of destroyed one dollar bills alone would be a whopping 200 miles high!
The bureau has dealt with the ashes of bundles of bills that were hidden in a mattress that caught fire when its occupant tried smoking in bed. In another instance, a farmer sent in the stomach of a cow that had consumed hundreds of dollars in cash, which the bureau's examiners were able to recover and replace. And you thought it was a lame excuse to claim that your dog ate your homework assignment!
If your currency is 50% intact or better, it's a routine matter. Less than 50%, you have a special case. Think about it for a minute... hmmm... "double your money..." hmmm
But even money shredded up can be redeemed. See your bank. Good luck!