You can be convicted of domestic violence from words alone. But regardless, law is just that -- law. It is not truth. That the law distinguishes between certain types of actions doesn't mean that distinction is philosophically defensible.
You are relying on a narrow definition of violence that makes your argument more or less circular. Here's how the World Health Organization defines violence: "the intentional use of physical force or power, threatened or actual, against oneself, another person, or a group or community, that either results in or has a high likelihood of resulting in injury, death, psychological harm, maldevelopment, or deprivation." This definition has been widely adopted, including in American statutes.
Again, what is the meaningful distinction between punching someone in the face and calling him or her a slur, if you know they will be equally harmful? Why would you call one "violence" and other "not violence" unless you were establishing some sort of technicality.