How do we take away parental rights in Wyoming?

Generally you don't. Getting a TPR is very difficult. Generally they are only granted to clear the way for an adoption or because the parent represents a danger to child.

If you give us more details of your situation we may be able to advise further.

We are wanting to take our sons mothers parental rights away so my wife can adopt him. We have full custody of him and she has lost her visitation due to drug violations.

Ok, then you get an attorney to prepare the adoption petition. As part of that petition he will prepare a request for a TPR. However, if she is unwilling to sign it may be very difficult. Even with the situation as you describe, a court may be reluctant to terminate her rights because there is a possibility of rehabilitation. Your attorney will know what your local courts are likely to do. That's why you NEED an attorney to handle this.