I've gotten the lawnmower stuck a half-dozen times trying to mow near this muck.
Since it's close to the pond, we can drain the water there. We do NOT want to drain sediment along with it - dredging a pond is expensive. Let's start by cleaning up the edges and adding a drain.
We dig a little deeper near the front so our drain can sit below the water table.
Cover the drain in gravel to stop the muck from ending up in the pond, then build a check dam with gravel and cement. This will cause a small, deep pond to form instead of a wide, shallow swamp.