If good-neighbor effort doesn't work, get a lawyer

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.