The LDS Church does not prohibit divorce; but it naturally warns that divorce is a last resort to be tried after using every possible measure to save the marriage. (Obviously, in some cases - e.g. abuse - this just won't be possible.)
Theologically, a "sealing" will only be valid in the eternities if both parties have honored their covenants during this life--so if a couple breaks their marital vows and divorces, the bond between the couple will be erased. However, as an administrative matter, the Church will usually leave the record of the sealing "on the books" until one party to the marriage or the other remarries, at which time they can apply for a "cancellation of sealing" prior to marrying the new spouse.
This is one of those days that the pages of history teach us are best spent lying in bed.
--Roland Young ("Uncle Willie"), The Philadelphia Story