Okay, I managed to cut the picture on my LJ. I just did what you'd do for a normal cut.

Left click above what you want to cut and drag down until you've got the entirety of what you want to cut outlined in blue. Then click on the LJ cut icon and type in whatever you want your cut phrase to be- I just used "art under cut" and then click okay.

I'm not the best at explaining things so I hope this helps!