Thank you so much for all of your help. I have used each and every piece of advice, combined them and have come up with the answer. Here is it:
Lock any portion of the artwork not affected by the cut out shape. (In my case, I have text and cut lines in the actual artwork that I don't want combined with the artwork being deleted.) Select all and group. Object expand appearance Object expand (keeping stroke and fill checked.) Object make compound path. Move a solid fill shape that matches the area to be removed over the artwork. (In this case, that would be the oval.) Select all. Click exclude in pathfinder shape modes. Deselect all by clicking away from the artwork. Click the area being cut away with the direct select tool and drag away. This moves the unwanted lines away from the artwork. Now click delete. There are some residual lines remaining within the oval, but they are no longer joined to the rest of the artwork and can easily be deleted with the selection tool or direct selection tool. Now unlock the shapes that were locked and you're done.