these do not naturally loose the dead fronds except after years of weathering, but these also tolerate pruning very well pretty much whenever you want to prune them. Ideally, you only prune dead leaves as a living leaf still is actively feeding the plant (or plants in your case... looks like you have three palms there). But most prune more extremely than that to decrease the frequency of pruning (nasty spines at the base sometimes make this less than a fun thing to do). Just don't do super extreme pruning as some do, leaving only a few fronds sticking straight up... that tends to be really hard on palms, though some will tolerate it.

I'd prefer not to prune it at all, except for dead fronds. Maybe just snip off the parts that are clearly dead (like the grey bits on the left-most leaf) and leave the rest of it alone?

Can't imagine why anyone would want to prune a pygmy date palm down to where it's just a mohawk -- don't people get these for the nice drapey look?