Not being funny or sarcastic but I would start all over and find the font you used.
It would seem to me it was done with good intentions but that it was not thought out well.
How do I eliminate the hidden masked areas of the photos for final art?
You can't. A raster image is by definition a rectangular array of pixels. If the shape you want is non-rectangular, all you can do is mask the unwanted pixels by either using a clipping path (the method you used), a file format that supports "transparent" pixels (GIF is not suitable for CMYK), a 1-bit color depth (won't work for your full-color textures) or alpha channel transparency (PNG is not suitable for CMYK. Use native PSD or TIFF).
Since your "diamond" shape is just a rotated rectangle (it is not square, though, if that was your intent--drag out a vertical guide and you'll see that the top and bottom points do not align), you could build the composite image as a single raster image, import it to your page layout, and rotate the single raster image there. That would negate any need for a clipping path, unless you need the voids between the different textures to be open. (Otherwise, you will still need a clipping path.)
However, the PDF you posted is not what you describe at all. The whole page is a raster image, sliced up into six slices.
Do you intend for this "logo" to be suitable for print reproduction? (It is entirely raster RGB.)
Thank you for the info. The pdf was made from the layout and only for viewing purposes. Originally I designed the logo as simple 4-color process vector art in Illustrator. A friend asked me to fill the shapes with these selections of raster glass images. So now I'm trying to make it work for print and web. Could I build the Illustrator file with placed cmyk glass images in the shapes, make clipping paths, save, copy & paste to Photoshop to save as a eps, tiff and gif? Wouldn't ps cmyk raster files work for print? Then how would I create a transparent background in ps? I know I've created problems for myself. Thanks for your guidance.
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You can trim the images to the bounding box of the clipping path, if that helps.
Release the clipping path from your image as you have it now, turn shape path to white fill with no stroke and set it's transparency to multiply. Select this shape and the image (shape is on top of image but ungrouped) and from the object menu select flatten transparency and set vectors to 100. Ungroup the result and delete the unwanted areas. Image is clipped to the bounding box of the shape path.
In the case of a rectangle --since its bounding box IS the rectangle -- you find the image is nicely cropped and all paths can be deleted.
You're instructions worked! That is exactly what I was trying to accomplish. Thank you for you assistance.