Remove taxes using Rules after coupon is redeemed
Yes, there is a core Drupal Commerce Rules action called "Remove taxes applied to a line item" in the Commerce Tax group. Additionally, via Rules you can inspect field values on any entity to see if they are empty or not. The coupons applied to an order are tracked through a variable called commerce_coupons.

Putting it all together, this means you need to create a custom product pricing rule that looks to see if the commerce_coupons field is non-empty. If so, it should use the action mentioned above to remove taxes. Make sure the weight of your custom rule is set such that it is calculated after the discount that gets added via the coupon.

Note: this cannot be achieved through the Commerce Discount module's interface. It must be done via Rules at Administration > Store > Configuration > Product pricing rules.