You will need to follow a double strategy: Prevention and remedial action. Which means in detail:
adequate fish load, even but rather restricted feeding, removal of plant debris by timely pruning plants,
use of a leaf protection net for the period of fall foliage, use of a skimmer to siphon pollen, flowers and leaves.
You should combine that with a filter system with pump which takes care of even bigger debris. A pond silt remover or suction cleaner is also a good solution to get rid of the mud. At any rate, you will lose some of the water in the pond which needs to be refilled. But you can use the extracted mud water as a nutrition liquid for compost or flower/vegetable beds.