No, you cannot go back to lower arena bracket. But you can remain on purpose in your current league for a long time, if you want, so you don’t find yourself overwhelmed again in the next one. Just keep your team power level lower than the point in which you advance. I linked the post showing the power level for each arena league.
Keep in mind that every buff to your heroes increases their power: leveling up, upgrading gear, upgrading active/passive skills.
You can level up your team to just before you get sent to new league and then stop improving that specific team for a while. Meanwhile you can work on your pets (they do not contribute to your team power), work on additional heroes you can use in dark rush, or just save a bunch of resources so you can quickly upgrade a lot once you do decide to progress to next league.