A difficult question to answer directly as I don't believe there is any sources which give a direct answer, but I can maybe enlighten you.

Vandalism could fall under public or private laws. If done to a public building then you would most likely have to speak with a Praetor and in my opinion be fined for the damage done. If done to someone elses private property then it would be handled between those involved although if serious enough you may have to get a magistrate involved. I remember reading that if you killed a slave/animal belonging to a person then you were expected to pay them back for that and if you damaged their property you were to pay them back within 30 days.

I don't have any sources but I can only imagine graffiti would go with a fine if punished at all. In Pompeii though they have found walls with things such as shopping lists enscribed on them along with traditional graffiti.