It will stop on its own eventually - these are best cut back late summer or in winter. I seem to remember reading something recently about immersing any leaking parts in water for a short time immediately after cutting - this apparently aids with stopping the bleeding. Might be worth a try, though I can't for the life of me recall exactly what was said.

As bamboo says it will stop eventually. Grape vines should only be pruned in the middle of winter to prevent this happening. Seaburngirl (another GoY member) prunes her on Christmas Day.

We cut the last 15 feet of our monster off in late November 09. No problem. This must happen when the sap rises in spring. Never have any problem with the bits I chop off in summer to stop it taking over the patio and help the grapes enlarge.

Yup it does Dorjac. By late November the sap would be back down in the roots.