Are you referring to Euonymus fortunei? If so, it is not a true vine (no vining parts) but has a single stemmed base. Technically, just a shrub but sometimes a widely spreading one. If allowed to grow upward unchecked, it can form aerial rootlets off the stems which help it adhere to various surfaces. Digging out the primary root ball and gently pulling the sprawling stems off of other plants should work just fine.

FWIW, this is most frequently pruned into a large rounded mound in my area or trimmed back routinely to keep as more of a manageable groundcover.