Assertion of a right can produce a fight, while a neighborly agreement for access will probably result in the work being done in a timely and peaceful manner.
[...] you can remove the part of the offending vine that is doing damage to your building.
Determining if you have a right to access the 20-foot exposed portion of your house abutting the neighbor's property is a legal question that we can't answer.
Common sense tells us you should have access in order to maintain your house, but to be absolutely sure we suggest you contact a real estate attorney.
There are a couple of things you should investigate prior to seeking legal advice.
[...] dig out the title insurance policy from when you purchased the house.
Review it to see if there is an easement allowing access to the adjoining property for maintenance purposes.
[...] because your situation is not uncommon in San Francisco, check with City Hall to see if a local ordinance addresses your situation.