CP, like other plants, can photosynthesize as long as the
leaves are green. I just trim back the dead parts. Rather
than do this now and again, I wait until the whole leave is
dead before cutting, so I do cut the whole leaf, but only after
it's dead.
You may not *need* to cut at all. If the plants are grown outdoors
the leaves will decompose over winter typically. Indoors I'd
definately trim back dead growth to prevent mould growth.
R.