Technically speaking, the civil divorce has no bearing on the get, and the get can be before or after the civil divorce. However, the accepted practice is to first complete all civil matters, pertaining to monetary issues, custody and other matters, and then to execute the get as the final step in the process. This has several reasons, some of which are based upon intricate Talmudic discussions concerning the get.
There is also an emotional factor that comes into play, with a lot of comfort when the entire process is completed with a religious act. A get can bring a profound feeling of closure to the relationship, as the couple feels, in a sense, that G-d has signed off on the process. In the Torah a get is referred to as a get krisus, which literally means a document of scission or cutting. With the giving of the get, the spiritual ties are formally cut. It’s healing for this to take place after all other issues have been completed, rather than there still being matters lingering.
Another reason is that there is always the hope that as the couple is going through the complicated legal issues, they will have a change of heart, and decide to stay together. The Talmud says that the altar sheds tears every time a couple is divorced, as the altar is the place of peace, and the couple has suffered a deep division. Therefore customarily the get is left for last, with hopes of reconciliation.
However, in a situation where it’s necessary to execute the get first, or concern that if it’s not done immediately then it might not be done at all — by all means the get should be performed before the other matters have been finished to ensure a kosher Jewish divorce.
With wishes of comfort and simcha.
Rabbi Yerachmiel Fried