Do Jehovah's Witnesses allow a person to divorce and marry someone else? Yes, divorce is permitted but if it is not on based on scriptural grounds, they are not free to remarry:
We adhere to the Bible’s view of marriage and divorce. God created marriage to be a permanent union between a man and a woman. The only Scriptural grounds for divorce is sexual immorality.—Matthew 19:5, 6, 9.
Even when elders are asked to help a couple deal with marital difficulties, they are not authorized to tell the couple what to do. (Galatians 6:5) However, someone who chooses to divorce without Scriptural grounds is not Scripturally free to remarry.—1 Timothy 3:1, 5, 12.
Separation is also permitted under the following circumstances:
Willful nonsupport.—1 Timothy 5:8.
Extreme physical abuse.—Psalm 11:5.
Absolute endangerment of spiritual life. For example, a spouse might try to force a Witness to break God’s commands in some way, and the threatened mate might decide that a separation is the only way to “obey God as ruler rather than men.”—Acts 5:29.
Source: "How Do Jehovah’s Witnesses View Divorce?"
If it is allowed only in some cases, what cases are those? As shown above, divorce is only allowed in the case of sexual immorality. If one marriage partner is sexually unfaithful, then the other marriage partner has grounds for divorce and re-marriage.
Will a congregation member get excommunicated if they divorce and marry someone else, or are there other consequences? A Jehovah’s Witness who divorces their partner because of sexual immorality and who subsequently remarries (another Jehovah’s Witness) will not be disfellowshipped, nor will there be any other consequences. However, eyebrows would be raised if they went on to marry someone who was not a Jehovah’s Witness. The Elders would be involved in discussing this with the Witness who wanted to remarry outside of the faith.
In the case of a Witness who separates from their partner because of “absolute endangerment of spiritual life” would they therefore be unable to remarry at any point in the future? From Jehovah’s Witness friends and family members I know, that would only be permissible if the partner of the Witness went on to commit adultery, for example, and a divorce ensued, based on those grounds.
Edit: Useful link Questions From Readers:
If a Christian divorces his wife without Scriptural grounds and then marries another person, how does the congregation view the previous marriage and the new marriage?