Show empathy. Showing empathy doesn't necessarily mean you agree with everything the person says. But it does mean you are willing to listen and to try to see things from the other person's perspective.
Don't argue. There is simply no point in arguing about hoarding. The harder you argue, the more the person is likely to argue back. The only solution is to get out of the argument.
Respect autonomy. Remember, most of you are dealing with an adult who has freedom of choice about her own possessions. Try to engage your loved one in a discussion (rather than an argument) about the home and her behavior. Ask your loved one what she wants to do, rather than just telling her what you want: "What do you think you would like to do about the clutter in the home?" "How do you suggest we proceed?"
Help the person recognize that his/her actions are inconsistent with her greater goals or values. Ask the person about her goals and values: "What's really important to you in life? How would you like your life to be five years from now? What are your hopes and goals in life?" Discuss whether the person's acquiring or difficulty organizing or getting rid of things fit with those goals and values. This is most effective if you ask, rather than tell: "How does the condition of your home fit with your desire to be a good grandmother? You've told me that friendships are very important to you; how well can you pursue that goal, given the way things are right now?"
If you have been accustomed to arguing and threatening and blaming, your new approaches will surprise your loved one, and it may take a little time before the person begins to trust you. Try these methods in several conversations and notice whether the balance seems to be tilting in the right direction. If so, be patient and keep up the good work.