I consider wild cucumber to be one of the very worst weeds... so invasive and literally strangles any other plant, including trees, that it gets a hold of! My gardening is on a farmstead and I throw most yard debris in a "pit" out behind the barn. I just pulled a huge quantity of wild cucumber (a very heavy mass of vine) in the roadside ditch. I would like to just leave it lay there to decompose. Question: can it re-root and start growing again?

I think there may be more than one plant known by the common name 'wild cucumber'. Are you asking about the spiky one? Echinocystis lobata?

It is an annual plant that will happily re-seed itself. The plant can be propagated from cuttings so my best answer would be 'yes, it can re-root'. Better to be safe than sorry.