There are a several ways to approach this, both for you and your partner.
Start by making peace with the fact that you can’t change someone else. In fact, if you push too hard your partner may become defensive, making the situation worse.
Instead, focus on getting what you need (perhaps a clutter-free space of your own?), modeling the benefits of hoarding-free behavior in your own life, and reinforcing positive change in your partner. The first post, below, is about working with a disorganized colleague, but the three tips are equally applicable to living with a stuff-loving partner.