Beaver dam removal is a potentially dangerous exercise and fraught with potential legal concerns.
Regarding legalities, disturbing a beaver dam can result in state and/or federal wetland violations. Always consult with government officials prior to disturbing any beaver dam. State Agencies
Dam removal can also cause severe property damage or loss of life; at best, it can be just a complete waste of time. If the beavers have been removed from the site and it has been determined that the dam needs to be removed, then you have several options. However, before employing the options, you should consider the downstream risks of rapidly removing a dam. Rapid dam removal can result in the collapse of other dams that are downstream. Rapid dam removal also causes erosion and other potentially negative environmental effects. Additionally, dam removal in the wintertime can result in the deaths of countless other species that rely on the frozen/cold pond to survive the winter.
1. Blasting the dam.
Some individuals are experienced in using explosives to remove dams. Of course, safety and legal concerns should be addressed prior to using this method.
2. Backhoe.
This technique can also result in rapid dam removal provided the equipment can reach the dam safely.
3. Hand removal.
Use a shovel and/or rake to take the dam down in stages. Although slower, it does offer the safer alternative to both the user and the environment. Simply cut several 6-inch-deep notches in the dam to let the water flow through. Come back each day to lower the dam some more.
Dams at culverts:
Be especially careful in removing dams from culverts. Avoid removing a dam from the downstream side as a catastrophic failure of the dam can result in the drowning of workers. Avoid entering a culvert to remove a dam by hand. It is better to use grappling hooks and pull the dam down from a safe distance and/or to use a telephone pole attached to a backhoe to push through the dam.
Remember, if the problem is water height and not tree damage, consider employing beaver pipes to control flooding.
Resources: (online)
ICWDM
Beavers
Beaver Pipes