What is the difference between them?
1. I can’t disown him as well as my grandmother.
2. I can no more disown him than I can disown my grandmother.

Question

Answer

With the first, you are saying you can't disown  both him AND your grandmother. There is a strong suggestion here that you have already disowned your grandmother. At the very least, you are considering disowning her, and you will not disown him as well.

With the 2nd, you are saying you would never disown him, just like you would never disown your grandmother.