You could try to build a sifter:
- Get a square meter/yard of 1/2" or 2cm wire mesh from the hardware store, "Chicken Wire" may work.
- Build a square frame that is a few inches smaller than your mesh.
- Staple the mesh to the frame
Then you can shovel your mud into the sifter and give it a good shake to separate the stones.
Here are some more advanced directions that include a wheelbarrow attachment/rail system if you're feeling adventurous.
There seems do be an undue amount of concern about using a sifter with wet soil/mud...
In my experience most mud will dry out to become, you know, just regular soil within 6-24 hrs.
Soils heavy in clay will require a lot more work:
- You could use more water to turn the clay into a slip or slurry while passing it through a sifter.
- You could wait for the clay to dry completely and starts to split into mudcracks. Then you can break it up a bit with a garden hoe and shovel it into a sifter. Your sifter in this case will very likely need to be re-enforced or built with a heavier gauge wire. Hardened dry clay will still crumble when shaken and agitated over the sifter and fall through leaving the rocks behind.
The soil in question doesn't appear to be terribly heavy in clay, at least judging by the color and granulation on the surface in the picture, and it doesn't appear to be terrifically wet either. It looks to be just damp topsoil, probably because it is a low lying area.
Some raking/tilling/hoeing before shoveling the soil into the sifter may make for easier going with the sifter, but it shouldn't be a big deal.