Without a clay liner to allow the water to be brought up close to the surface, it will just stay at ground water elevation. If the ground water is close to the surface, you may not want to line it and just rely on the ground water to maintain the water level.
Mud ponds are typically much larger than the one you are proposing. They rely on small fish populations and mother nature to filter the small amount of waste. As you get smaller, then it becomes more like a typical liner pond and needs to have filtration to process the ammonia, and other wastes, and a mud pond is going to be muddy, so it cannot be processed through our normal filter systems.
Koi like to excavate looking for the bugs, crayfish, and other natural foods, and will widen the mud pond over time, filling in the bottom, so it is a good idea to make the slopes fairly flat going down to the bottom. If the top were only 8 foot wide at the top, then the maximum depth would probably be no more than 2 foot safely. I would recommend that site be made into another liner pond, rather than a mud pond. Just not enough room.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard