You can use them on your alts. Just save them. You can also craft goods for merchantry using Mystical Crystal. And you can use it for your Collection. I know A new collection is out needing the Mystical Crystals. There might be an update in the future for crafting abyssal crystal from mystical crystals so hold on tight to it.
New update:
You can hoard these mystical crystal chest and open it using the function in your inventory that lets you auto fuse. Just make sure you set it on your setting before opening, for 1000 mystical chest I got 17 abyssal crystals (red crystal)