I believe all those red spots that are on your car after you park it under a tree are actually a result of the byproducts of bugs found in the trees rather than sap.
Either way, it's a bitch to remove. I had this problem badly on my last car, a mark V golf GTI.
I tried everything. Eventually, the only effective way I could remove it was actually with a scotch brite pad rubbing moderately. Make sure the car is completely clean first (apart from the marks you're trying to remove anyway). I can't remember if I used lubricant or water or nothing at all but probably safest would be to try with some lubricant first.
I didn't end up damaging my paint but theory would suggest you definitely could.
Try clay first though.