Illustrator ... cutting raster images. help

you can cut them manually using "Crop Image" button. Select your image, press Crop Image button and move the proxies to your desired size.

I wrote a script for a client that needed a similar thing for Print on Canvas project. PM me if you're interested in an automated solution.

I recommend bypassing Illustrator and using Photoshop instead.  You will most probably need to add bleed between the joins for a little overlap when the tiled image is applied to whatever.  I sense this is a grand format wall mural to be printed  and cut.  I have seen an inch bleed.  The Illustrator file can house each tiled image along with trim marks.  That file can then be converted to PDF or RIP and printed as is.  Do yourself a favor and work with whoever is printing the job.  Ask them why they want the image sliced and diced in Illustrator.

case 1:

if you want to cut them without moving each one separately:

Draw 3 rectagles on the top of the image, then make them as a compund path,  ( select them without the image) by pressing right click -> make compound path or

object -> compound path -> make

then select the compund path and the image together ,  right click -> make clipping mask ( ctrl + 7 )

case 2: to move each one separately:

you need 3 copies of rectangle and 3 copies of the image

Put each rectangle on the top of the image, select them both and make clipping mask ( ctrl + 7 )

repeat the same steps on the second and the third rectangle.