Piper's video dealing with how a wife might deal with an abusive husband went viral enough that Steve has, at length, decided to address the topic of grounds for divorce contra Piper's lines of argument. It's a pretty short blog post considering it was written by Steve, and is worth reading.
As a teaser to perhaps inspire you to read the rest, dear reader, here's a short snippet at the end that may inspire you to read Steve's much lengthier preliminary discussion of application:
xiii) In application to the specific issue at hand:
a) Domestic violence is a travesty of what marriage represents, in terms of companionship as well as the emblematic significance of marriage (i.e. to illustrate God’s devotion to the redeemed). It’s the antithesis of how marriage is supposed to function (e.g. Eph 5:22-33).
b) Breach of covenant can nullify a covenant if one party fails to honor the terms of the covenant. And this isn’t the case of a spouse who makes a good faith effort, but falls short due to sin. Rather, this is acting in bad faith.
c) There is also an argument from analogy. A battered slave could be manumitted (Exod 21:20-21). A fortiori, a battered wife can divorce her husband. What’s true in the lesser case of a slave is true in the greater case of a wife, for a wife has greater rights than a slave.
There's more but I threw in the conclusion in the hopes of inspiring you to read how Steve builds up to this excerpt. It's pretty short for him, as noted earlier. :)