The Catholic Church does not promote divorce. It does not, however, stop a person from obtaining a divorce, and if possible the Church will try to assist the parties in reconciling (Retrouvaille).
As far as the sinfulness of obtaining a divorce, the Church holds that a party may, or may not be sinful in filing for and obtaining one, and that is subject to the specific circumstances.
As far as getting a divorce if one’s spouse has committed adultery (which is what I presume you are addressing, OP), some parties can reconcile and move forward. Normally that takes some extensive time and counseling. it is easy to suggest that the immoral party is the sole source of the adultery, but there is very often a dynamic within the marriage that has been at play. This is not to suggest that adultery is ever justified; but there often are times that there has been a dynamic, not addressed, which has pushed the immoral party to consider outside sexual activity.
If the parties get a divorce, the Church will not grant a decree of nullity based on the adultery. It will only base it on a defective consent or impediment existing as of the day of the marriage. If it can be show that as of the day of the marriage, the adulterer had no intention of exclusivity, the subsequent adultery may possibly be evidence of that defective consent, but not solely as the only evidence.
And without a decree of nullity, the parties are not free to marry someone else; in spite of a state decree of divorce, the parties are presumed still married.