| If you plan to use the piece again as the cover, it will be trickier. Basically, you need to draw a line that you plan to follow for your cuts. Using a very tiny drill bit, like 1.5mm, carefully drill about six holes in a line along your cutline.
Once they are drilled, you should be able to push through with a jigsaw blade and then can carefully saw along the line. Watch for depth. Ensure you use the thinnest jigsaw blade you can find, as you want the gap to be very tight.
Once you're finished and have the piece out, you can glue small scraps underneath the edge of the cutout on the guitar body and your cover should fit pretty neatly. There will be a narrow gap all the way around it though... | 
