After you complete TW3 main story can you still play?

After approaching the Isle of Mists (I won't say anything about that to prevent spoiler) the most secondary quests are lost, but some remain. There are some interesting DLCs too, which I might like to complete after game ends. There are 3 endings for Ciri, one of them makes me wonder if Geralt will still be able to roam the world and play purchased DLCs.

Do you have to create a new save and start over - or you can just continue playing the left story? I have already almost finished the game in my old save, but it corrupted just before being able to finish the game.

It doesn't matter which ending you get. You will still be able to finish off the side quests and do all the DLC.

Some of your choices in the main game have an effect on the very end of the Blood and Wine DLC quests.