May a divorced Catholic remarry his or her ex-spouse?
The simple answer is, yes, of course, because a civil (secular) divorce does not end the marriage, which is a sacrament of lifelong union. In fact, this would be the ideal situation when, for serious reasons, a couple had a civil divorce (or separation) with the hope that someday the grave reasons that required so dire a measure as divorce would be overcome and they could get back together.
In fact, there is not even the need for a new wedding on the part of the Church, since the man and woman are still married. Even so, there may need to be a new civil arrangement for renewing the legal effects of marriage, if that is desired. But this is not a strict moral requirement. The couple is always free to come together physically since they are morally still married, but if they want the financial and tax effects of marriage civilly, then they have to approach the civil authority for that.
It should be noted that if there is an innocent party, say in the case of adultery, he or she by coming together again physically by that very fact have given up the claim of divorce or separation. This means that relations between divorced or separated spouses should be in view of their coming back together again permanently as soon as they are able.
There is one serious reservation, however. If the marriage broke up the first time because of some defect which made the first union invalid, then that defect has to examined and dealt with, but if there was no such defect, then the couple is free to return to a life together.