All Beliefs are Welcome Here!
With a bit of luck, its not a real link, rather you miss/like/even love them and now they're gone. Time and distance will heal that wound.
If you have an actual link to the person there are two ways to break it, one of them will kill you and the other might kill you. A. Commit suicide. B. Raise a barrier through (yes through) the link, the pain will make you wish you'd died. And then there's the bad news, it doesn't always work, depending entirely on how strong the link is. Then of course there is the effect raising the barrier will have on the other person, generally bad, very bad. If they are the stronger of the two of you, it won't hurt them much. If they are the more weak you might kill them.
The best answer I have for you is to send them away, and if you are not the dominant power then leave and go far far away. Distance will lessen the pain, and depending on how powerful you are it might be possible to go far enough the link and pain will fade.
Violet Flame of Transmutation - its been discussed recently on the forums.
It will permanently sever any connection that is not made out of pure light or unconditional love. I would visualize the connection between the two of you, perhaps like a large cable, and you're cutting it with a purple bladed lightsaber (slowly, so it feels like work is being done).