My mailmate shredder from Staples has jammed and I can't figure out how to unjam it.

This appears to be a shredder rather than a Car and Trucks issue. I have moved you to the correct category and edited your question for clarity.

Remove the head and vacuum all the dust and paper bits, top and bottom. There is a sensor in there that is looking for a sheet of paper. When you turn it on, it thinks it has found it. While you are at it, oil the blades.

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There are tips here... http://www.abcoffice.com/office-equipment-news/2011/01/how-to-clear-a-jammed-paper-shredder/
or here... http://www.wikihow.com/Unjam-a-Paper-Shredder

drive is seized-remove power cord- open cover rotate cutting drum slowly using motor drive gears - look for debris/gear teeth missing

Having the same Problem!

All shredders shut down within afew seconds if they do not detect paper inserted. Safety feature.

I’m happy to help further over the phone at https://www.6ya.com/expert/jayw_0e86fb055a7b73de

There is a 10mm 5amp @ 250v fuse on the main board that is probally blown . I unsoldered mine and soldered a pigtail fuse holder with a convient sized 5 amp fuse inside in its place . The shredder is not too bad to take apart , the head comes apart from the body of the shredder .Turn it upside down and you will see 6 or 7 phillips screws .Once these are removed the head assembly opens up and you will see the circuit board which is held in place by 2 phillips screws. A quick ohm meter test will reveal the fuse condition. It was an easy fix just MAKE SURE YOU KEEP THE UNIT UNPOWERED while you work on it or its unassembled.

Try adding a lube, such a WD40, it may reduce the friction enough to break free. Spray it above and below and as needed during the operation.
Work the jam back and forth, removing what you can as it pops out, power off the machine before reaching into the blades.

Hope this helps
Ed