You can build a guitar with just a jigsaw. It will do everything you need to do, it just won't do it as well as a scroll saw or bandsaw. The biggest problem with a jigsaw is that the blade is only fixed at one end. It stays fairly perpendicular when cutting straight, but will get pretty crooked cutting curves, especially in thick materials. If you are going to use a jigsaw, cut well outside your lines and sand-in.
Here I am getting ready to cut fret slots. I have marked the fret locations along the centerline, just to confirm that everything is right. Below that is my fret slotting guide. It is a 1" piece of aluminum, precisely drilled with a series of holes based on the standard mathematical formula for fret locations, which you can look up, or use one of the online calculators. I made a spreadsheet of it. The holes are numbered along the top, with the corresponding scale length below. The interesting ones are: (rounded-off)
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