Most professional foam manufacturing that requires cutting, rather than injection molding, uses a hot-wire cutter. An electric signal is put through a wire pulled snugly between two points. The foam is fed past the wire as the heat cuts through it to create a smooth face on either side of the wire. Hot-wire cutters can also be formed to cut profile shapes in the foam for products such as crown molding. Hot-wire cutters can be built to almost any size. For example, they are used to cut slices from giant blocks to make the 2-inch thick foam insulation available from home improvement stores.
Band saws, table saws, jig saws and reciprocating saws can all be used to make fairly smooth cuts through foam. In particular, thin-bladed jig saws and band saws are good for intricate cuts, especially curves. Since the saws will remove a small amount of foam, called a kerf, it is best to keep a shop vac handy and work in areas where foam dust will not be a major issue. Allow the foam to settle out of the air and sweep or vacuum it up after cutting.
Almost any bladed tool will cut foam. Carpenter's cross-cut saws work almost as well as power saws, albeit much slower. Mark the line you want to cut with a permanent marker and check your cut path regularly, making adjustments as necessary. Use a saw with a blade that is at least one-third longer than the foam you are cutting is thick.
To create three-dimensional sculpted pieces, tools such as electric chain saws are good for bulky, rough cutting. Remove bits of foam, similar to whittling or carving. Once the basic shape is arrived at, tools such as rasps and grater-style planes work well for finer details. Routers and smaller rotary tools are ideal for the fine details that may be required. Surfaces can also be smoothed with power sanders.