I have a Skimmia that produces both berries and flowers, but I don't know which one.
I has some faded berries on it, should these be cut off or left to fall off naturally?
I suppose if you want to tidy it up and the berries have died off there would be no reason why you shouldn't cut them off. I can't imagine it doing any harm to the plant.
Just leave the berries to drop off,there is no benefit in cutting them off.
Doesn't matter either way, but if the berries are left they germinate often before dropping and can be planted in a seed tray.
I used to have a Skimia hedge which I kept to a regular height by pruning annually, cutting alternate branches/shoots as they only flower on previous seasons growth, so if you cut all of the new growth you miss a season's flowers and berries.
I think Alan10's suggestion is the best compromise