According to NBC News, it is illegal to tear up or mutilate a dollar bill. The crime of destroying any legal tender is punishable by a fine of up to $100 or jail time of up to six months. Enforcement of this law is conducted by the Secret Service.
NBC News identifies the applicable law as Title 18, Section 333 of the United States Code. The primary reason behind the restriction toward the destruction of dollar bills and other currency denominations is the cost of replacing the destroyed bills. Each note costs approximately 0.05 cents to print, with the government currently printing about 37 million notes daily.