I've never found a need or reason to cut my dip tubes. Unless you get a LOT of fallout, there's almost nothing to suck up the tube.
My dry hopping is done with a bag, so again there's really nothing mucking up the bottom to cause me any concern.
Primary: English Mild
On tap: Pale Ale, Lancelot's Wheat, English Brown Ale, Steam Beer, HoovNuts IPA
Bottled: MOAM, Braggot, Raspberry Melomel, Merlot, Apfelwein, Pyment, Sweet mead, Cabernet
Gal in 2009: 27, Gal in 2010: 34, Gal in 2011: 13, Gal in 2012: 10