I used a jig saw to cut both the outline and limb taper on a board bow ............once.
Granted, I didn't have a top-shelf jig saw but I was sure I had permanent nerve damage in my right forearm after that experience.
Since then my trim carpenter nephew gave me an old Craftsman band saw that is also probably not top-shelf but with a new heavy duty blade it cuts boards and even staves like the hot knife thru butter.
Like John said, I would use a coarse rasp before using the jig saw again.