How to destroy a chest using redstone in minecraft?

Solution 1:

In order to drop the contents of a chest, it must be actually destroyed. The only way to destroy specific blocks using redstone devices is to use pistons to accomplish one of these things:

• Remove the support of a block that is attached to another block.
• Attempt to move blocks such as plants and torches, which drop instead of moving. (Interestingly enough, this property doesn't seem to relate to anything else — most such blocks are insta-break and washed away by water, but e.g. pumpkins aren't; conversely, attached blocks such as rails and trapdoors may be moved as long as the destination also has a valid attachment point.)
• Remove the support of a falling block and drop it onto an invalid location.

Since chests have none of these properties, your idea of TNT is probably the only way to destroy chests on command.

However, given your purpose, you could probably effectively use droppers (or dispensers) instead, and have a completely reusable system with no blast shielding. A single dropper holds only 9 stacks, but you can expand its capacity by connecting it to a chest via a hopper; this is limited by the hopper's transfer rate, but multiple parallel chest/dropper systems will take care of that.

Simply connect a suitable number of droppers, facing a water stream or open shaft above you, to a single redstone clock, and adjust the period of the clock so that you get the appropriate rate of paper output. Etho's Trading Hut (thanks @BlaXpirit for the link) is an example of such a construction (made in the pre-hopper days, so it uses many dispensers alone); it's very large, but the size only depends on how much paper you want to trade.

Solution 2:

You can use minecart with chest. To destroy a cart, let a skeleton shoot it