You're forgetting that a previous marriage is in the past. What's done is done.
Jesus does not acknowledge divorce, so there is no such thing as a "previous marriage." A civil divorce is a sham that is not recognized by God. Someone who obtains a civil divorce and remarries is, in God's eyes, still married to their first spouse and is therefore committing adultery.
If a Christian has already divorced and remarried, meaning they are living in a state of adultery, the only course of action is to repent, meaning to stop sinning. Hopefully that would simply mean moving out and obtaining a civil divorce. However, in some cases there are children involved and it is important not to pass the harm along to innocents. In such cases, the couple would have to find a way to live together as brother and sister.
Now that said, it is sometimes the case that the first marriage wasn't actually valid in God's eyes. It may have been perfectly legal (meaning that the children are not bastards). For example, two men may legally marry, but in God's eyes it is not a real marriage. In the Catholic Church, these men may therefore divorce civilly and obtain an annulment from the Church stating they never had a sacramental marriage in the first place. Then each of these men may then marry a woman and it will be considered their first marriage.
There is a serious serious problem in Protestant churches in that there are "marriages" that have ended in civil divorce which were never valid in the first place, meaning that the persons have every right to marry again, but their churches have no structure in place in which to evaluate marraiges to see if they were valid or not. This is horribly unjust. It has led to many rightfully remarried Protestants giving the appearance of living in sin
The following are the grounds for nullifying a marriage in the Catholic church (stating it was never a real marriage in the first place, regardless of its legality):
Insufficient use of reason (Canon 1095, 10) You or your spouse did not know what was happening during the marriage ceremony because of insanity, mental illness, or a lack of consciousness.
Force (Canon 1103) You or your spouse married because of an external physical or moral force that you could not resist. Fear (1103) You or your spouse chose to marry because of fear that was grave and inescapable and was caused by an outside source.
Fraud (Canon 1098) Reasons for Marriage Annulment You or your spouse was intentionally deceived about the presence or absence of a quality in the other. The reason for this deception was to obtain consent to marriage.
Grave lack of discretionary judgment concerning essential matrimonial rights and duties (Canon 1095, 20) You or your spouse was affected by some serious circumstances or factors that made you unable to judge or evaluate either the decision to marry or the ability to create a true marital relationship.
Psychic-natured incapacity to assume marital obligations (Canon 1095, 30) You or your spouse, at the time of consent, was unable to fulfill the obligations of marriage because of a serious psychological disorder or other condition.
Ignorance about the nature of marriage (Canon 1096, sec. 1) You or your spouse did not know that marriage is a permanent relationship between a man and a woman ordered toward the procreation of offspring by means of some sexual cooperation.
Error of person (Canon 1097, sec. 1) Reasons for Marriage Annulment You or your spouse intended to marry a specific individual who was not the individual with whom marriage was celebrated. (For example, mail order brides; otherwise, this rarely occurs in the United States.)
Error about a quality of a person (Canon 1097, sec. 2) You or your spouse intended to marry someone who either possessed or did not possess a certain quality, e.g., social status, marital status, education, religious conviction, freedom from disease, or arrest record. That quality must have been directly and principally intended.
Total willful exclusion of marriage (Canon 1101, sec. 2) You or your spouse did not intend to contract marriage as the law of the Catholic Church understands marriage. Rather, the ceremony was observed solely as a means of obtaining something other than marriage itself, e.g., to obtain legal status in the country or to legitimize a child.
Willful exclusion of children (Canon 1101, sec. 2) You or your spouse married intending, either explicitly or implicitly, to deny the other's right to sexual acts open to procreation.
Willful exclusion of marital fidelity (Canon 1101, 12) You or your spouse married intending, either explicitly or implicitly, not to remain faithful. Willful exclusion of marital permanence (Canon 1101, sec. 2) You or your spouse married intending, either explicitly or implicitly, not to create a permanent relationship, retaining an option to divorce.
Future condition (Canon 1102, sec. 2) You or your spouse attached a future condition to your decision to marry, e.g., you will complete your education, your income will be at a certain level, you will remain in this area.
Past condition (Canon 1102, sec. 2)R You or your spouse attached a past condition so your decision to marry and that condition did not exist; e.g., I will marry you provided that you have never been married before, I will marry you provided that you have graduated from college.
Present condition (Canon 1102, sec. 2) You or your spouse attached a present condition to your decision to marry and that condition did not exist, e.g., I will marry you provided you don't have any debt.
Error regarding marital unity that determined the will (1099) You or your spouse married believing that marriage was not necessarily an exclusive relationship.
Error regarding marital indissolubility that determined the will (Canon 1099) You or your spouse married believing that civil law had the power to dissolve marriage and that remarriage was acceptable after civil divorce.
Error regarding marital sacramental dignity that determined the will (Canon 1099) You and your spouse married believing that marriage is not a religious or sacred relationship but merely a civil contract or arrangement.
Lack of new consent during convalidation (Canons 1157,1160) After your civil marriage, you and your spouse participated in a Catholic ceremony and you or your spouse believed that (1) you were already married, (2) the Catholic ceremony was merely a blessing, and (3) the consent given during. the Catholic ceremony had no real effect.