If you made a Jpg before importing in Illustrator, why aren't you importing in photoshop ? to my knowledge photoshop is better suited to clip / slice/ cut certains pieces. You don't have to worry about the quality of your jpg since it is already an image and photoshop is made to edit image, not illustrator.
If it was a Illustrator vertoriel file with a lot of data in it, photoshop would be a very bad choice, but in your case i think it is the best.. if you have photoshop.
As far as illustrator, i am not aware of any option that allow you to slice or cut certain pieces.... but i can be wrong.
Message was edited by: Chorale0001
Photoshop is the better tool for this. However, there are convoluted workarounds that can be used in Illustrator to accomplish this task. A search here should uncover several discussions on this topic.
It sounds to me like the OP is looking for a way to clone out or cover up
certain elements in the jpg image, not actually slice it into smaller
pieces. Even so, Photoshop is a better tool for this.