Tigerpaws, to answer your question - ask somebody that knows! That somebody isn't me, but I will render my opinion.
I think the mandolin chop is mostly for rhythm especially in Bluegrass and other musical genre that have a big rhythm component(Jazz or Blues?). Supposedly, when not taking a break, the mandolin player often emphasises the off-beat with a cut-off chop chord. You have to do a four fingered chord since you are actually damping the strings and an open string will ring more than you want.
However, on most breaks and other genre of music you don't need the chop chords.
Now for the really important question that has puzzled musicans for eons! Why is the kitchen device that chops and slices vegetables called a mandolin? Does it have any thing to do with "chop" chords?