Absent the neighbor's permission, you cannot cut the rosebush under California law, whether it is touching your wall or not. While you have his oral acquiesence by his statement that it was "your responsibility", I would require his express permission in written form. I would also want his general permission in written form to access is property in order to repair the wall.
If the wall in entirely on your property, it is your sole responsibility to repair (even though it may be providing benefit to the neighbor as well). If the wall is on the property line and you did not construct it, there may be an argument for shared repair, but that might be more trouble than it is worth given your neighbor's unhelpful disposition. It would also require a survey to prove it's location.
Please let me know, if you have follow-up questions.
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