Note: See @MosheL's answer for a modern solution.
Old Answer (and probably still needed for SHOUTcast):
I've found that with SHOUTcast/Icecast streams, the only way to guarantee that you won't be playing from cache is to use the old method of adding a cache-busting URL parameter.
If your original stream URL is this:
http://1.2.3.4/someMountPoint
Then use JavaScript to generate a URL like this when playing:
http://1.2.3.4/someMountPoint?nocache=123456789
This ensures that caching will not happen, as to the browser, they are different resources.