Jay,
You can do the dirty destructive deed, with the Clipping Mask selected (exact way depending on version):
1) In the Transparency palette/panel dropdown list select anything but Normal (Multiply is fine); this step is undoubtedly unneeded in your version, you may try without it;
2) Object/Edit>Flatten Transparency, just keep the defaults including 100% Vector;
3) Shudder (optional, unless unavoidable).
This will crop everything to the Clipping Path, so everything outside is actually gone, but a raster image can only be rectangular regardless of where/how it is created so it will have transparency/emptiness to fill its Bounding Box.