Use a utility knife to cut your polyurethane foam to shape. Extract the blade from the knife by using your thumb to push the blade lever up toward the top of the knife. Press the blade into the foam and run the blade down the foam making your preferred cut. Depending on the thickness of your polyurethane foam, a utility knife might not cut deep enough. If this is the case, flip the foam over and use the utility knife to cut the other side, following the same cutting path.
Cut the polyurethane foam using a hand saw. Place the foam on a saw horse to allow space for the saw to cut through the foam. Place the saw at the edge of the foam where you wish to cut. Angle the hand saw at a 45-degree angle and move your arm back and forth to cut the foam. The more teeth on the hand saw, the cleaner your cut will be.
Use a hand-held router with a steel or carbide cutting tip to cut shapes in the center of the polyurethane foam. Set the hand-held router on top of the foam in the area where you wish to cut in the center of the foam. Flip the power switch and guide the hand-held router to design and cut shapes in the center of the foam.