I've installed many simple devices in order to control the water in beaver ponds. The device is known as a Clemson Pond Leveler and can be found by doing a Google search on the internet. It is basically a piece of large diameter (8" or bigger) PVC pipe with a 90 degree elbow on the downstream side with another pipe (stand pipe) in the elbow that controls the height of the water inside the pond (inside the dam) according to the length of the stand pipe. To drain the pond, you simply pull the stand pipe from the elbow, plant your crop, allow it to mature, then replace the stand pipe to again fill the pond. All of this is dependent on a water source coming into the pond. I assume that the pond was filled originally by a stream that the beavers dammed up, but high water draining over the dam busted a hole in it. If the beavers have abandoned the pond, you will have an easier time keeping the outflow opening free of debris and the beavers clogging it up. There still needs to be a screen of some type to protect the opening from getting clogged with items draining through it. You would need to cover the pipe tightly with a clay based soil to prevent a wash out around the pipe and another blowout in the dam. Packing the soil as you rebuild the hole/blowout will ensure better success.
Here is a crude sketch of the leveler. A couple of stakes on either side of the elbow aids in keeping the elbow and standpipe verticle.
Here is a link to the pond leveler infohttp://www.clemson.edu/psapublishing/PAGES/AFW/AFW1.PDF