Remove the frame from around the hot tub frame. Most have side panels that pull away for easy access. If your hot tub is set into a deck, you will have to get underneath the deck to access the panels.
Cut away large chunks of the insulation using a drywall saw. The blade will be sharp enough to cut the insulation but not sharp enough to cut plumbing pipes.
Bag up the chunks of insulation in garbage bags to get them out of the way.
Scrape the remaining insulation with a chisel. This can be labor intensive and take a good deal of time.