Removing Tree Sap from a Tombstone

Try GooGone. I don't know what it will do to the Granite, but it will remove the sap.

I would contact the caretaker of the cemetery, maybe they have an idea, also they may remove the tree. How can the tree be there, roots possibly growing into the grave sites, caskets? If roots can penetrate our water/sewer pipes, they have no invasion problem anywhere else.
Cemetery stone is an expensive item to replace ($3000-5000) in the very least. Be careful of what you use. We just use water and paper towel. Elbow grease.

Granite is a porous stone. I would contact a monument company and have them clean it and see if there's something they can seal it with.

I would try vinegar to remove the sap. My car was covered with sap and vinegar got it off without too much effort. As far as the staining, if the granite is smooth or not too porous, try a damp Mr. Clean magic eraser. Might sound too simple but it's worth a try because I just used one to take blue permanent marker off of my parents' brand new solid wood dining table. They never found out my daughter was coloring at that table when her ink bled through! I have to tell you I was sceptical but also desperate so I tried and it worked!