I was thinking something along the lines of muttering "thank god I don't need you anymore" whilst dropping it in the bin, followed by eating cheesecake.
The most important part of the ceremony would be the cheesecake.
I haven't needed my mooncup since I had a hysterectomy 7 months ago, but I am strangely reluctant to bin it. I also don't need 1 and 1/2 boxes of sanitary towels, the pregnancy test or anything else period related that's hiding in the bathroom cupboard.