I don't see a problem. Just save the left and right side as .png and the rest (middle) as .jpg.
Edit: Almost forgot to tell you HOW.
You can use slices...
I've talked about everything concerning slices already, when I made Website Building - Slicing & Dicing
in another thread.
The n00by Way.
You take the rectangle marque tool and mark the central area then you left click and select Layer via Cut. The select either the left or right side and do the same. (don' have to be exact just make sure it's all covered)
Now you have 3 portions of the sig on 3 layers.
Deselect all then just select one go Image
save it... then undo from before the trim, and do the same for the rest. All done.