Savage mufflers appear to be prone to chirping. My used 2001 began doing it shortly after I bought it.
I believe something comes loose internally due to rust. I'm not sure if you can get into it to fix it.
The best solution is to replace it. The preferred replacement on this site is to replace it with a Harley Dyna muffler. They are available cheap as used take-offs. The swap is pretty simple. Mine bolted up fine without needing adapters. I did only use one of the mounting holes on the muffler bracket, instead of both holes. If you get a dyna with the baffle plate still in it, they are a little louder than stock, but not obnoxious. They are also well-made with good chrome and no packing to burn out.
There is a good discussion/tutorial in the tech section.
Adding link to Dyna thread.
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1298689417