The Soundproof Cubical
About the only practical silencer for a saxophone is to build a soundproof practice room. This may not be nearly as bad as it sounds.
If you have room in your abode, the soundproof practice room can actually be a cubical build of nothing more than a 2x2 frame covered with Styrofoam insulation sheets on the outside. The cost of that can be really inexpensive. And it can all be assembled with drywall screws and an screwdriver bit in an electric drill. Just build a cube large enough to play the sax in. Screw the insulation sheets onto the outside of the 2x2 frame. Then on the inside hang old blankets on all four walls and the ceiling and floor. You'll need to make provision for ventilation so you don't suffocate in there. Maybe even mount a little fan to circulate in fresh air. It's not going to be 100% soundproof, but it should knock the sound down to acceptable levels. How big of a project this sounds to you will of course depend upon your own construction skills. This is a really easy project and could be hired out to a local handyman or whatever.
I thought I might elaborate a little bit on this, just in case anyone reading this decides to go this route.
Some construction hints:
When building the cubical, build each of the four walls separately. To do this will require twice as many 2x2's but it's worth the extra investment if you'll ever be moving this thing around. The reason being that the four walls can then be screwed together as units, forming the cubical, and then disassembled in the same way. The Styrofoam sheets, and even the blankets can be attached to each wall before the cube is assembled.
For a door, you can simply hinge an entire wall, (the roof holding the other 3 walls in place, or build one of the walls in two sections, one second serving as the door. Then just hinge the door.
You'll also need to mount a light inside. Use a cool light, like a florescence bulb. Something that isn't going to get so hot to catch the blanket walls on fire.
You might want to strap a fire extinguisher on the bell of the sax. That way you can keep practicing whilst putting out the fire.
*Use fire-retardant blankets. ;}
If you heat it in the winter, consider any fire hazards associated with your heating source too. One of those electric oil-filled heaters would probably be the best ticket. No red-hot source there. Plus it's clean air too.
Think ahead when considering your design.