Courts do not usually deny requests to dissolve a marriage, even if that request is only coming from one spouse. Nevertheless, if your spouse wants a divorce but you don’t, you can argue that the marriage is not “irretrievably broken” at the evidentiary hearing. The district judge will make the determination; however, most divorce attorneys will tell you not to be optimistic about your chances of stopping the divorce by making this argument, assuming one spouse still wants the divorce.
Conversely, there is no way to finalize your divorce through mediation alone. Even if you reach a tentative agreement in mediation, this agreement must be formalized in a written stipulation, signed by both parties and their attorneys, and ultimately approved by the Court.  This signed stipulation — not your verbal agreements from mediation sessions — is what becomes the enforceable terms of your divorce, and should be prepared or at least reviewed and revised by your lawyer before you sign.
A party who is dissatisfied with the court's decision may ask the trial judge to change his or her decision or set a new trial or appeal to the Court of Appeals. No new evidence or testimony is taken by the Court of Appeals. Appeals are hard to win. Usually when the Court of Appeals overrules a trial judge, it is because the Court of Appeals believes the trial judge made a mistake about the law.