President Trump has legal and executive authority under US and International Law to do as he did.
It may not be popular, and might even be the wrong thing to do...but he is within his authority.
The terms of the Agreement (Treaty if you wish....) facilitate any individual Nation a part of the Agreement to cite issues and take action if it feels there was not a proper response to those concerns.
Yale Journal of International Law | Is the Trump Administration Bound by the Iran Deal?