I guess that depends on what you mean by “light mud.” Are you saying that you stirred up the crud on the bottom of the pond and now the water is murky? Or do you mean mud, like you would need a shovel to remove?
Some sump pumps (not meant for continuous use) can handle varying degrees of “dirty” water. And there are some pond/waterfall pumps that are rated as “solids” pumps. Now, as far as which pumps work best, you just need to do some internet research. Just be sure it (whatever pump you get) is rated for “solids-handling,” or “dirty water” use.