It's an example of emphasis by repetition.
A major theme of the Crow cycle is how empirical methods of understanding the cosmos are doomed to failure in a spiritual sense. It doesn't matter how well science untangles the mysteries of nature: it brings humanity no nearer to being able to deal with the big questions of life and death.
Owl's song is an example of this. The owl "sings" the world to total destruction but then (in the unquoted climax of the poem) the rocks and stars of his song come alive again:
Seeing the clawtrack of star
Hearing the wingbeat of rock
Hence his efforts have been in vain: his failure makes him afraid.
The line you're trying to untangle is the climax of a series of escalating negatives. First we have:
how the swan blanched forever
This is a small thing. Swans are already white, "blanched". But the choice of word also implies a more extreme process, boiling (we "blanch" vegetables in boiling water).
How the wolf threw away its telltale heart
Is more extreme. The wolf, another living animal, has its heart sung away.
We then come to more inorganic, generalised distant forms, whose destruction is more difficult and, with each passing line is "sung" in a more extreme fashion. Until we come to:
The rock surrendered its last hope
The world is made of rock. Hope is foundational to the positive human experience. This is thus an image of extreme desolation, of total unmaking. Then, finally:
And cold died beyond knowledge
If there's one thing more universal and general than rock, it's cold. The cold of the dark vacuum left when the world is unmade. If cold can "die", we are at the uttermost end of physical existence. There is nothing left.
The repetition of these lines highlights the growing extremity of what owl is attempting. The final line is thus a signal of ultimate emptiness, where there is no longer even basic physics to apply.
This is also the meaning of "beyond knowledge". If the laws of physics no longer apply, we have no way of understanding, of "knowing" what that state is like, or how it came to be.
EDIT: As user @Randal'Thor very helpfully observers, all these lines are self-negating, fitting with and emphasising the negative picture that's being built up. The swan is already white. The wolf, in mythic tradition, is a "heartless" predator. Air has no appearance and water creates numbness.
THE POETRY OF TED HUGHES, P. E. Strauss, Theoria: A Journal of Social and Political Theory, No. 38 (May 1972), pp. 45-63