Is there a function to save and replay Duels?

Yes, there is a Replay Function that will let you save and replay Duels.

After a PVP Duel, you will be able to Save your Duel in the Duel Results menu by clicking Save Duel. To access your Duel Replays, on the Main Menu, select your profile and select Replay to see a list of all of the Duel Replays you have on your account.