The Bible on divorce in the case of spousal abuse
If you are looking for clear and direct statements in the Bible allowing for divorce in the case of spousal abuse, that is going to be difficult if not impossible. The Bible was written in cultures that accepted a husband's right to discipline (read: "beat") his wife as he saw fit. Spousal abuse as we define it today was not seen as cause for divorce in the cultures of the Bible. For those Christians who read the Bible very literally, it is hard to put together a convincing case for divorce in the case of spousal abuse based on the Bible alone.
However, for those Christians who are willing to read the Bible more broadly and less literally, a case can be made based on a broader biblical definition of the words "fornication" and "adultery."
Relevant statements based on a literal interpretation of the Bible
Since the Bible was written in a very different time and culture than that of today, it is hard to draw a straight line between the few biblical injunctions about marriage and divorce on the one hand, and marriage and divorce as they exist in today's society on the other.
For example, Deuteronomy 24:1-4 speaks of a man who is displeased with his wife writing her a certificate of divorce. According to Matthew 19:7-8; Mark 10:2-5, this was interpreted as a commandment of Moses allowing a man to divorce his wife. However, there was no similar commandment allowing a woman to divorce her husband. For all practical purposes, in Old Testament times only men, and not women, had the right to divorce their spouse.
And yet, by the time 1 Corinthians 7:8-16 was written in New Testament times, women had apparently acquired the right to leave, or divorce, their husbands as well.
Further, Jesus specifically repudiated the Mosaic law of divorce in Matthew 19:7-9; Mark 10:5-9; Luke 16:18, establishing the principle historically adhered to by various Christian denominations that divorce is allowed to husbands and to wives only in the case of adultery.
However, even this is not necessarily seen as a hard and fast rule. In New Testament times as in Old Testament times, a divorced woman was in a difficult and dangerous position. It was very common for divorced women to be forced into prostitution because they would be disowned by society and family alike. Therefore Jesus' strong stance against divorce can be read as protecting women from that fate at the hands of "hard-hearted" men, rather than as a blanket prohibition of divorce except in the case of adultery that was intended to stand for all time. In Western cultures today, divorce, while still a difficult experience, has nowhere near the devastating consequences for women that it did in Bible times.
And indeed, 2 Corinthians 6:14-18 strongly suggests that the acceptable reasons for divorce are broader than adultery when that is defined exclusively as sexual unfaithfulness:
Do not be yoked together with unbelievers. For what do righteousness
and wickedness have in common? Or what fellowship can light have with
darkness? What harmony is there between Christ and Belial? Or what
does a believer have in common with an unbeliever? What agreement is
there between the temple of God and idols? For we are the temple of
the living God. As God has said:
"I will live with them and walk among them, and I will be their God,
and they will be my people." (Leviticus 26:12; Jeremiah 32:38;
Ezekiel 37:27)
Therefore,
"Come out from them and be separate, says the Lord. Touch no unclean
thing, and I will receive you." (Isaiah 52:11; Ezekiel 20:34,
41)
And,
"I will be a Father to you, and you will be my sons and daughters,
says the Lord Almighty." (2 Samuel 7:14; 7:8)
The quotation of, "Come out from them and be separate, says the Lord. Touch no unclean thing, and I will receive you," can be read as supporting divorce in the case of believers being married to unbelievers--which does not necessarily involve sexual infidelity.
However, even this is a difficult reading, since 1 Corinthians 7:10-16 indicates that believers (Christians) are not to divorce unbelievers if the unbeliever is content to live with them, but that believers are freed from the bonds of marriage if the unbeliever leaves the marriage.
Relevant statements based on a broader, less literal interpretation of the Bible
In present-day culture, "fornication" and "adultery" are used almost exclusively of sexual unfaithfulness to a partner--"fornication" if no one involved is married, and "adultery" if one or more of the people involved are married.
However, in Bible times, "fornication" and "adultery" were also used more broadly to mean unfaithfulness to God and to God's commandments. For example:
Yet they would not listen to their judges but prostituted themselves
to other gods and worshiped them. They quickly turned from the ways of
their ancestors, who had been obedient to the Lord’s commands. (Judges
2:17)
And:
When the Lord began to speak through Hosea, the Lord said to him, "Go,
marry a promiscuous woman and have children with her, for like an
adulterous wife this land is guilty of unfaithfulness to the Lord."
(Hosea 1:2 - and see the rest of the book of Hosea)
If we use the broader scriptural definition of fornication, adultery, and unfaithfulness, then there is a clearer path to a broader definition of the allowable causes of divorce. That definition would allow for divorce in the case of errant unfaithfulness to God and to the laws of God, among which is the commandment not to commit adultery.
If "adultery" means "being unfaithful" in the broader scriptural sense, then any major ongoing violation of the marriage vows and of God's commandment to love our neighbor as ourselves (which certainly includes our spouse!) is adultery in the biblical sense of the word.
The clearest indication of this broader meaning of adultery in relation to marriage, and specifically in relation to violence associated with marriage, is in the difficult-to-translate passage Malachi 2:10-17:
Have we not all one father? Has not one God created us? Why then are
we faithless to one another, profaning the covenant of our ancestors?
Judah has been faithless, and abomination has been committed in Israel
and in Jerusalem; for Judah has profaned the sanctuary of the Lord,
which he loves, and has married the daughter of a foreign god. May the
Lord cut off from the tents of Jacob anyone who does this—any to
witness or answer, or to bring an offering to the Lord of hosts.
And this you do as well: You cover the Lord’s altar with tears, with
weeping and groaning because he no longer regards the offering or
accepts it with favor at your hand. You ask, "Why does he not?"
Because the Lord was a witness between you and the wife of your youth,
to whom you have been faithless, though she is your companion and your
wife by covenant. Did not one God make her? Both flesh and spirit are
his. And what does the one God desire? Godly offspring. So look to
yourselves, and do not let anyone be faithless to the wife of his
youth. For I hate divorce, says the Lord, the God of Israel, and
covering one's garment with violence, says the Lord of hosts. So take
heed to yourselves and do not be faithless.
You have wearied the Lord with your words. Yet you say, "How have we
wearied him?" By saying, "All who do evil are good in the sight of the
Lord, and he delights in them." Or by asking, "Where is the God of
justice?"
Here divorce is associated with faithlessness, profaning the covenant and the sanctuary, marrying those who adhere to other gods, violence ("covering one's garment with violence"), and generally doing evil in the sight of the Lord.
Superficially, Malachi 2:10-17 can be (and commonly has been) read as a diatribe against divorce. But a more careful reading suggests that it is a diatribe against all sorts of evil, unfaithfulness, profanation, and violence that lead to the destruction of marriage both in the collective sense of the church's marriage to Christ and in the individual sense of marriage with a wife or husband.
In short, if we read the injunctions of the Bible against fornication and adultery more broadly, as speaking not only of sexual infidelity, but any kind of major ongoing unfaithfulness to God and to our spouse, this can provide a biblical basis for divorce in the case of spousal abuse and other major violations of the vows of marriage and the commandments of God.
For more on Malachi 2:10-17 in relation to marriage and divorce, see my article, "God Hates Divorce" vs. "Do Not Be Unfaithful to the Wife of Your Youth."
(This answer is written from the perspective of a contemporary understanding of the Bible in harmony with the theology of Emanuel Swedenborg (1688-1772) as commonly understood in the more liberal of the denominations that follow Swedenborg's theology.)