You actually want an Opacity mask, not a Clipping mask.
Clipping masks are hard edged, always.
Opacity mask can have, well, opacity tweaks.
It is not possible to "feather" a clipping mask path, or apply any sort of transparency alteration to the path. Transparency is simply not supported for Clipping masks. Clipping masks only see the spine of the path, nothing more.
To create an Opacity mask....
- Draw a circle over all your artwork (like you would if making a clipping mask.)
- Fill the circle with 100C100M100Y100K (registration) or R0G0B0.
[Opacity masks are a rare case where you actually want 100% of ink in CMYK mode
because it's a mask and not artwork which will output]
- Apply the feather to the circle
- Select everything
- On the Transparency panel click the
Make Mask button.
- You may then need to tick the
clip options on the Transparency Panel (depends on art).
This will make your circle an Opacity mask. You'll see the mask thumbnail in the Transparency panel. To edit the mask, you click the mask thumbnail. To go back to editing artwork, click the artwork thumbnail.
Note: Although any transparency in the Opacity Mask will be flattened upon output, the mask itself can be built using standard vector shapes and it all remains vector while working. You can also use raster images for Opacity masks (but not clipping masks).
Possibly further assistance: