To start, DOD stands for Department of Defense which includes many agencies, including the Army, Navy, Marines and Air Force, amongst others. A DOD Approved paper shredder is really the same thing as an NSA approved shredder. See this post for more info.
The NSA decides what shredders meet their requirements and at this time the DOD follows what the NSA says when it comes to security. Basically, a DOD Approved Shredder is the same thing as and NSA Approved Shredder which are also known as high security paper shredders and/or security level 6.
For more detailed information on DOD Approved Paper Shredders visit the links below:
NSA/CSS Specification 02-01 – Extensive information and data on NSA shredder specs
“Maximum Particle Dimensions: 75% of the shredded particles shall have no edge dimension exceeding 5 millimeters in length. The remaining particles may exhibit edge dimensions between 5 and 12.5 millimeters in length.”
List of NSA Approved Shredders
List of Approved Media Destruction Devices
“Top Secret = 0.8 x 11.1 mm (1/32″ × 7/16″) no longer approved after 1 October 2008 for U.S. government classified documents”
All About Shredders – Basic info on high security shredders
“Most of the major manufacturers are listed: Capital Shredder Corp., Cummins-Allison, Dahle, Ecco, Fellowes, HSM/Geha, Rockville/Marquis, Olympia, SEM, Whitaker/Destroyit/Intimus, and others.”
The Shredder Guide – misc paper shredder info
“DOD shredders are designed to shred sensitive and top secret documents. These paper shredders offer you the greatest degree of protection against information theft or misuse by reducing your private documents to mere confetti.”
[...] What is a DOD Approved Shredder? [...]