I have a 16GB iPad mini that fills up quickly. Large podcasts files which are downloaded as new episodes come are not helping my case. So here’s what I did and what you can do if you have the similar problem.
1. Go to Settings>Podcasts.
2. Under the Podcasts tab. You will notice that Download Episodes is set to Only New.
3. Set it to Off.
And that’s it! Enjoy your podcasts without worrying that they’re eating up your storage. :)