Using the heavy duty knife, cut the bead off the inside of one side of the tire.
Cut slits, scallops, or triangle shapes out of the inside of the now bead-less side of the tire.
Grab one notch, "petal" or "v," and begin pulling. Use your knee or foot on the opposite side of the tire to create leverage.
As the section of tire you are pulling back begins to move, slide your hands over to the next notch/petal/v shape and pull it back.
Working with the tire as it begins to bend itself (don't rely on brute force) continue working your way around the edge of the tire until it is entirely inverted.