If you want to remove it slowly (or in sections), I have found using a siphon hose works well for sand but you will be doing major water changes at the time. Slowly scouping with a Solo cup works for the first couple of open inches but you will still muck up the water (not a big deal if you have been stirring the sand bed, if not you stand a chance of exposing dangerous bacteria in the deaper dead areas). I have used a long automotive funnel to replace/add substrate with better luck than just dumping but I don't know if anything will help with mud. Hopefully Thales will have some suggestions but I think he started with an empty (as in no occupants) tank when he created his environment.