Remove the edge from u to its parent:
function cut(u)
access(u)
// u's parent is the rightmost node in left subtree
if u.left is not null
u.left.parent := null
u.left := null
After access(u), the path from u to root is in one auxiliary tree. u's left subtree contains all ancestors. By detaching it, you cut u from its parent.
Alternative (cut edge u-v):
function cut(u, v)
makeRoot(u)
access(v)
// Now u is direct left child of v
v.left.parent := null
v.left := null
Time: amortized.