You mentoned that the beavers have backed up the water in the field. Obviously there is water flowing into the pond that they have backed up. The beaver dam will be holding the water higher than the other water allowing for you to place a "Clemson Pond Leveler" through the dam. I have installed at least 6 of these devices and they do work! They allow you to drop the water down (out of the field) for planting, corn, rice, millet, etc., then turn the elbow back in the upright position, place the proper size piece of pvc joint, to flood the field when you desire........just prior to or during duck season. When you cut the groove out of the beaver dam and place your PVC pipe in the groove, the beavers will repair the damage overnite and stop the water from flowing. Then when you are ready to drop the water level, just turn down the elbow and let the water flow. You must place the cylindrical screen (I use 2x4 mesh) over the upstream opening and the holes in the PVC so the beavers can't stop it up.
Here's some info that gives complete directions and instructions on the construction in a pdf format for easy printing. Make sure you anchor it down and get it as level through the dam as possible for best possible results. Be prepared to see lots of little beavers appear when you open up the groove in the dam. "Many little hands make light work!!" Make sure you do the whole job of installing the pipe and screen and elbow the first day 'cause they'll close it off, pack it with mud and stop the water overnight.http://files.dnr.state.mn.us/assistance ... eveler.pdf
Good luck and good shooting!